Indian Statistical Institute Series – serie

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.

This book discusses recent developments in mathematical programming and game theory, and the application of several mathematical models to problems in finance, games, economics and graph theory. All contributing authors are eminent researchers in their respective fields, from across the world. This book contains a collection of selected papers presented at the 2017 Symposium on Mathematical Programming and Game Theory at New Delhi during 9–11 January 2017. Researchers, professionals and graduate students will find the book an essential resource for current work in mathematical programming, game theory and their applications in finance, economics and graph theory. The symposium provides a forum for new developments and applications of mathematical programming and game theory as well as an excellent opportunity to disseminate the latest major achievements and to explore new directions and perspectives.

This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance. The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics. The book discusses in-depth topics such as quadratic variation, Ito formula, and Emery topology. The authors briefly addresses continuous semi-martingales to obtain growth estimates and study solution of a stochastic differential equation (SDE) by using the technique of random time change. Later, by using Metivier–Pellaumail inequality, the solutions to SDEs driven by general semi-martingales are discussed. The connection of the theory with mathematical finance is briefly discussed and the book has extensive treatment on the representation of martingales as stochastic integrals and a second fundamental theorem of asset pricing. Intended for undergraduate- and beginning graduate-level students in the engineering and mathematics disciplines, the book is also an excellent reference resource for applied mathematicians and statisticians looking for a review of the topic.

This book is a blend of recent developments in theoretical and computational aspects of group theory. It presents the state-of-the-art research topics in different aspects of group theory, namely, character theory, representation theory, integral group rings, the Monster simple group, computational algorithms and methods on finite groups, finite loops, periodic groups, Camina groups and generalizations, automorphisms and non-abelian tensor product of groups. Presenting a collection of invited articles by some of the leading and highly active researchers in the theory of finite groups and their representations and the Monster group, with a focus on computational aspects, this book is of particular interest to researchers in the area of group theory and related fields of mathematics.

This book focuses on the application of data mining techniques in cricket. It provides detailed examples of how data mining can be helpful for decision-making in sports with special reference to cricket, particularly the quantitative features related to Twenty20 cricket, the latest and the most popular format of the game. The book highlights the performance quantification of cricketers (batsmen, bowlers, all-rounders, and wicket keepers), determining the market valuation of cricketers based on their on-field performances and the effect of age on the performance of the cricketers. It also provides a comprehensive overview of the different aspects of the game where quantitative techniques are beneficial, and highlights the use of statistical and data mining tools in analysing sports-related data and objective decision-making in sports. The book appeals to a wide readership, including postgraduate students of statistics/mathematics, data analysts, sports management bodies. It also offers data miners, such as researchers in statistics, mathematics, operations research, and computer science ideas for projects.

This book focuses on the application of data mining techniques in cricket. It provides detailed examples of how data mining can be helpful for decision-making in sports with special reference to cricket, particularly the quantitative features related to Twenty20 cricket, the latest and the most popular format of the game. The book highlights the performance quantification of cricketers (batsmen, bowlers, all-rounders, and wicket keepers), determining the market valuation of cricketers based on their on-field performances and the effect of age on the performance of the cricketers. It also provides a comprehensive overview of the different aspects of the game where quantitative techniques are beneficial, and highlights the use of statistical and data mining tools in analysing sports-related data and objective decision-making in sports. The book appeals to a wide readership, including postgraduate students of statistics/mathematics, data analysts, sports management bodies. It also offers data miners, such as researchers in statistics, mathematics, operations research, and computer science ideas for projects.

The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field.  It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.

The book offers a comprehensive introduction to Leavitt path algebras (LPAs) and graph C*-algebras. Highlighting their significant connection with classical K-theory—which plays an important role in mathematics and its related emerging fields—this book allows readers from diverse mathematical backgrounds to understand and appreciate these structures. The articles on LPAs are mostly of an expository nature and the ones dealing with K-theory provide new proofs and are accessible to interested students and beginners of the field.  It is a useful resource for graduate students and researchers working in this field and related areas, such as C*-algebras and symbolic dynamics.

This book discusses the state-of-the-art techniques in the domain of contact tracing applications. Well known in the field of medical science, this topic has received attention from governments, industries and academic communities due to the COVID-19 pandemic. This book provides a link between new proposals related to contact tracing applications and a contextual literature review primarily from the cryptologic viewpoint. As these applications are related to security and privacy of individuals, analyzing them from cryptologic viewpoint is of utmost importance. Therefore, present developments from cryptologic aspects of most proposals around the world, including Singapore, Europe, USA, Australia and India, have been discussed. Providing an in-depth study on the design rationale of each protocol, this book is of value to researchers, students and professionals alike.

This book discusses the state-of-the-art techniques in the domain of contact tracing applications. Well known in the field of medical science, this topic has received attention from governments, industries and academic communities due to the COVID-19 pandemic. This book provides a link between new proposals related to contact tracing applications and a contextual literature review primarily from the cryptologic viewpoint. As these applications are related to security and privacy of individuals, analyzing them from cryptologic viewpoint is of utmost importance. Therefore, present developments from cryptologic aspects of most proposals around the world, including Singapore, Europe, USA, Australia and India, have been discussed. Providing an in-depth study on the design rationale of each protocol, this book is of value to researchers, students and professionals alike.

This book is a collection of selected papers presented at the consecutively held international conferences on “Game Theory and Networks”, organized by the Department of Mathematics, Dibrugarh University, India, in collaboration with the Economics Department of Queen’s University, Belfast, UK, during September 6–9, 2019 and September, 13–15 2018. The book includes chapters on network measures and network formation, application of network theory to contagion, biological data and finance and macroeconomics as expository articles. The book also contains chapters on fair allocation in the context of queuing, rationing and cooperative games with transferable utilities for engaged researchers. A few survey chapters on non-cooperative game theory, evolutionary game theory, mechanism design and social choice theory are also incorporated to cater to the needs of the beginners in the field.This book discusses the use of game theoretic tools and network models across disciplines: mathematics, statistics, economics, computer science, political science, sociology and psychology. It aims at providing a suitable learning experience to beginners on the basics of cooperative games, networks and mechanism design, as well as recent developments to research scholars having the basic knowledge of these topics.

This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.

This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.

As a comprehensive textbook in survey sampling, this book discusses the inadequacies of classic, designed-based inferential procedures and provides alternative approaches in the form of model formulations, model-design-based procedures of analysis, inference and interpretation. The book focuses on a wide range of topics which included Bayesian and Empirical Bayesian approaches, complex procedures of stratification, clustering, sampling in multi stages and phases, linear and non-linear estimation of parameters, small area estimation by spatial and chronological modelling, network and adaptive sampling methods and more. The book includes detailed case studies and exercises, making it valuable for students of statistics, specifically survey sampling.

As a comprehensive textbook in survey sampling, this book discusses the inadequacies of classic, designed-based inferential procedures and provides alternative approaches in the form of model formulations, model-design-based procedures of analysis, inference and interpretation. The book focuses on a wide range of topics which included Bayesian and Empirical Bayesian approaches, complex procedures of stratification, clustering, sampling in multi stages and phases, linear and non-linear estimation of parameters, small area estimation by spatial and chronological modelling, network and adaptive sampling methods and more. The book includes detailed case studies and exercises, making it valuable for students of statistics, specifically survey sampling.

This book prepares students to execute the quantitative and computational needs of the finance industry. The quantitative methods are explained in detail with examples from real financial problems like option pricing, risk management, portfolio selection, etc. Codes are provided in R programming language to execute the methods. Tables and figures, often with real data, illustrate the codes. References to related work are intended to aid the reader to pursue areas of specific interest in further detail. The comprehensive background with economic, statistical, mathematical, and computational theory strengthens the understanding. The coverage is broad, and linkages between different sections are explained. The primary audience is graduate students, while it should also be accessible to advanced undergraduates. Practitioners working in the finance industry will also benefit.

This book prepares students to execute the quantitative and computational needs of the finance industry. The quantitative methods are explained in detail with examples from real financial problems like option pricing, risk management, portfolio selection, etc. Codes are provided in R programming language to execute the methods. Tables and figures, often with real data, illustrate the codes. References to related work are intended to aid the reader to pursue areas of specific interest in further detail. The comprehensive background with economic, statistical, mathematical, and computational theory strengthens the understanding. The coverage is broad, and linkages between different sections are explained. The primary audience is graduate students, while it should also be accessible to advanced undergraduates. Practitioners working in the finance industry will also benefit.

This book includes speeches given during five seminar sessions held in honor of Prof. C. R. Rao, on his 100th year. This book also contains a few write-ups touching on the diverse aspects of this august personality. The chapters pay tribute to Prof. C. R. Rao, the Padma Vibhushan awardee, by discussing his life and contributions to the field of statistics. The book also includes a chapter by the Abel Prize winner Prof. S. R. Varadhan who happened to successfully complete his Ph.D. under the guidance of Prof. C. R. Rao.

This book includes speeches given during five seminar sessions held in honor of Prof. C. R. Rao, on his 100th year. This book also contains a few write-ups touching on the diverse aspects of this august personality. The chapters pay tribute to Prof. C. R. Rao, the Padma Vibhushan awardee, by discussing his life and contributions to the field of statistics. The book also includes a chapter by the Abel Prize winner Prof. S. R. Varadhan who happened to successfully complete his Ph.D. under the guidance of Prof. C. R. Rao.

This book provides a chronological, comprehensive, and up-to-date review of indirect methods of data collection from the human population such as randomized response, non-randomized response, item count, item sum, nominative, and negative questioning techniques. Such surveys include questionnaires on sensitive issues such as domestic violence, the history of induced abortion, involvement in fraud, plagiarism, affiliation with political parties, opinion of government policies, and religious practices, to name a few. The book also studies methods of drawing inferences from such data. The methods provided in the book can be applied to any complex survey design and a wide class of estimators. This book may serve as a handbook of indirect survey methodologies, as readers may receive a wide spectrum of materials from this book alone. Most of the randomized response (RR) techniques are described with the aid of diagrams so that readers can easily understand the randomization techniques, their applicability, and their complexity in real surveys. Applications of different indirect survey methodologies in various areas are presented.

This book provides a chronological, comprehensive, and up-to-date review of indirect methods of data collection from the human population such as randomized response, non-randomized response, item count, item sum, nominative, and negative questioning techniques. Such surveys include questionnaires on sensitive issues such as domestic violence, the history of induced abortion, involvement in fraud, plagiarism, affiliation with political parties, opinion of government policies, and religious practices, to name a few. The book also studies methods of drawing inferences from such data. The methods provided in the book can be applied to any complex survey design and a wide class of estimators. This book may serve as a handbook of indirect survey methodologies, as readers may receive a wide spectrum of materials from this book alone. Most of the randomized response (RR) techniques are described with the aid of diagrams so that readers can easily understand the randomization techniques, their applicability, and their complexity in real surveys. Applications of different indirect survey methodologies in various areas are presented.

This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon–Nikodym and Jordan–Hahn theorems, providing a detailed account of 𝐿𝑝 spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions.The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea’s theorem and Kolmogorov’s consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.

This book covers major measure theory topics with a fairly extensive study of their applications to probability and analysis. It begins by demonstrating the essential nature of measure theory before delving into the construction of measures and the development of integration theory. Special attention is given to probability spaces and random variables/vectors. The text then explores product spaces, Radon–Nikodym and Jordan–Hahn theorems, providing a detailed account of 𝐿𝑝 spaces and their duals. After revisiting probability theory, it discusses standard limit theorems such as the laws of large numbers and the central limit theorem, with detailed treatment of weak convergence and the role of characteristic functions.The book further explores conditional probabilities and expectations, preceded by motivating discussions. It discusses the construction of probability measures on infinite product spaces, presenting Tulcea’s theorem and Kolmogorov’s consistency theorem. The text concludes with the construction of Brownian motion, examining its path properties and the significant strong Markov property. This comprehensive guide is invaluable not only for those pursuing probability theory seriously but also for those seeking a robust foundation in measure theory to advance in modern analysis. By effectively motivating readers, it underscores the critical role of measure theory in grasping fundamental probability concepts.

This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.

This book focuses on research in linear algebra, statistics, matrices, graphs and their applications. Many chapters in the book feature new findings due to applications of matrix and graph methods. The book also discusses rediscoveries of the subject by using new methods. Dedicated to Prof. Calyampudi Radhakrishna Rao (C.R. Rao) who has completed 100 years of legendary life and continues to inspire us all and Prof. Arbind K. Lal who has sadly departed us too early, it has contributions from collaborators, students, colleagues and admirers of Professors Rao and Lal. With many chapters on generalized inverses, matrix analysis, matrices and graphs, applied probability and statistics, and the history of ancient mathematics, this book offers a diverse array of mathematical results, techniques and applications. The book promises to be especially rewarding for readers with an interest in the focus areas of applied linear algebra, probability and statistics.

This book provides an overview of statistical concepts and basic methodology for the study of genetics of human traits and diseases. It attempts to provide a step-by-step description of problem identification, study design, methodology of data collection, data exploration, data summarization and visualization, and more advanced analytical methods for inferring genetic underpinnings of human phenotypes. The book provides codes in R programming language for implementation of most of the statistical methods described, which will enable practitioners to perform analysis of data on their own, without having to mold the data to fit the requirements of commercial statistical packages. Useful to anyone engaged in studies to understand and manage good health, the book is a useful guide for sustainable development of humankind. Primarily intended for practicing biologists especially those who carry out quantitative biological research, in particular, human geneticists, the book is also helpful in classroom teaching.

This book provides an overview of statistical concepts and basic methodology for the study of genetics of human traits and diseases. It attempts to provide a step-by-step description of problem identification, study design, methodology of data collection, data exploration, data summarization and visualization, and more advanced analytical methods for inferring genetic underpinnings of human phenotypes. The book provides codes in R programming language for implementation of most of the statistical methods described, which will enable practitioners to perform analysis of data on their own, without having to mold the data to fit the requirements of commercial statistical packages. Useful to anyone engaged in studies to understand and manage good health, the book is a useful guide for sustainable development of humankind. Primarily intended for practicing biologists especially those who carry out quantitative biological research, in particular, human geneticists, the book is also helpful in classroom teaching.