Samuel Karlin – författare

The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.

This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.

New to this edition:

Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process Realistic applications from a variety of disciplines integrated throughout the text Extensive end of chapter exercises sets, 250 with answers Chapter 1-9 of the new edition are identical to the previous edition New! Chapter 10 - Random Evolutions New! Chapter 11- Characteristic functions and Their Applications

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems.New to this edition:- Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications- Plentiful, completely updated problems- Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers- New chapters of stochastic differential equations and Brownian motion and related processes- Additional sections on Martingale and Poisson process- Realistic applications from a variety of disciplines integrated throughout the text- Extensive end of chapter exercises sets, 250 with answers- Chapter 1-9 of the new edition are identical to the previous edition- New! Chapter 10 - Random Evolutions- New! Chapter 11- Characteristic functions and Their Applications

The purpose, level, and style of this new edition conform to the tenets set forth in the original preface. The authors continue with their tack of developing simultaneously theory and applications, intertwined so that they refurbish and elucidate each other.The authors have made three main kinds of changes. First, they have enlarged on the topics treated in the first edition. Second, they have added many exercises and problems at the end of each chapter. Third, and most important, they have supplied, in new chapters, broad introductory discussions of several classes of stochastic processes not dealt with in the first edition, notably martingales, renewal and fluctuation phenomena associated with random sums, stationary stochastic processes, and diffusion theory.

This Second Course continues the development of the theory and applications of stochastic processes as promised in the preface of A First Course. We emphasize a careful treatment of basic structures in stochastic processes in symbiosis with the analysis of natural classes of stochastic processes arising from the biological, physical, and social sciences.

Population Genetics and Ecology is a collection of papers presented at a 1975 conference-workshop held in Israel and is devoted to topics in population genetics and ecology. Contributors discuss topics related to population genetics and ecology, including the determinants of genetic variation in natural populations; experimental design and analysis of field and laboratory data; and theory and applications of mathematical models in population genetics. The book describes a number of field and laboratory studies that focus on a variety of spatial and temporal character and enzyme frequency patterns in natural populations, along with possible associations between these patterns and ecological parameters. This volume is organized into three sections encompassing 31 chapters and begins by summarizing the results of field and laboratory research that investigated gene frequency patterns in space and time of animal and plant populations. This book then explains the origin of new taxa; animal and plant domestication; variation in heritability related to parental age; and problems in the genetics of certain haplo-diploid populations. The next section offers a combination of data analyses and interpretations of related models, with some papers devoted to the origin of race formation and the interaction between sexual selection and natural selection. Among the theoretical studies presented are facets of selection migration interaction; stochastic selection effects; properties of density and frequency dependent selection; concepts and measures of genetic distance and speciation; aspects of altruism; and kin selection. This book will be of interest to naturalists, experimentalists, theoreticians, statisticians, and mathematicians.

This book deals with a key area of population genetics: the ratio of the sexes in a population, or the allocation of resources to male versus female reproductive function. Samuel Karlin and Sabin Lessard establish the formal theoretical aspects of the evolution of sex ratio within the constraints of genetic mechanisms of sex determination. Their results generalize and unify existing work on the topic, strengthening previous conceptions in some cases and, in other instances, offering new directions of research. There are two main approaches to understanding the causes and effects of sex ratio. One approach focuses on the optimization and adaptive functions of sex allocation, while the other emphasizes the consequences of genetic sex determination mechanisms. In discussing the utility of these two approaches, Professors Karlin and Lessard examine the principal sex-determining mechanisms and facts involved in sex ratio representations, the various genetic and environmental factors that contribute to adaptive sex expression, and the evolution of sex determining systems and controls.From a population genetic perspective, the authors derive evolutionary properties in support of the high incidence of 1:1 sex ratio in natural populations and investigate the conditions that can explain the occurrence of biased sex ratio.

An Introduction to Stochastic Modeling, Revised Edition provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.

Matrix Games, Programming, and Mathematical Economics deals with game theory, programming theory, and techniques of mathematical economics in a single systematic theory. The principles of game theory and programming are applied to simplified problems related to economic models, business decisions, and military tactics. The book explains the theory of matrix games and some of the tools used in the analysis of matrix games. The text describes optimal strategies for matrix games which have two basic properties, as well as the construction of optimal strategies. The book investigates the structure of sets of solutions of discrete matrix games, with emphasis on the class of games whose solutions are unique. The examples show the use of dominance concepts, symmetries, and probabilistic arguments that emphasize the principles of game theory. One example involves two opposing political parties in an election campaign, particularly, how they should distribute their advertising efforts for wider exposure. The text also investigates how to determine an optimal program from several choices that results with the maximum or minimum objective. The book also explores the analogs of the duality theorem, the equivalence of game problems to linear programming problems, and also the inter-industry nonlinear activity analysis model requiring special mathematical methods. The text will prove helpful for students in advanced mathematics and calculus. It can be appreciated by mathematicians, engineers, economists, military strategists, or statisticians who formulate decisions using mathematical analysis and linear programming.

Mathematical Methods and Theory in Games, Programming, and Economics, Volume II provides information pertinent to the mathematical theory of games of strategy. This book presents the mathematical tools for manipulating and analyzing large sets of strategies. Organized into nine chapters, this volume begins with an overview of the fundamental concepts in game theory, namely, strategy and pay-off. This text then examines the identification of strategies with points in Euclidean n-space, which is a convenience that simplifies the mathematical analysis. Other chapters provide a discussion of the theory of finite convex games. This book discusses as well the extension of the theory of convex continuous games to generalized convex games, which leads to the characterization that such games possess optimal strategies of finite type. The final chapter deals with the components of a simple two-person poker game. This book is a valuable resource for mathematicians, statisticians, economists, social scientists, and research workers.

Studies in Econometrics, Time Series, and Multivariate Statistics covers the theoretical and practical aspects of econometrics, social sciences, time series, and multivariate statistics. This book is organized into three parts encompassing 28 chapters. Part I contains studies on logit model, normal discriminant analysis, maximum likelihood estimation, abnormal selection bias, and regression analysis with a categorized explanatory variable. This part also deals with prediction-based tests for misspecification in nonlinear simultaneous systems and the identification in models with autoregressive errors. Part II highlights studies in time series, including time series analysis of error-correction models, time series model identification, linear random fields, segmentation of time series, and some basic asymptotic theory for linear processes in time series analysis. Part III contains papers on optimality properties in discrete multivariate analysis, Anderson''s probability inequality, and asymptotic distributions of test statistics. This part also presents the comparison of measures, multivariate majorization, and of experiments for some multivariate normal situations. Studies on Bayes procedures for combining independent F tests and the limit theorems on high dimensional spheres and Stiefel manifolds are included. This book will prove useful to statisticians, mathematicians, and advance mathematics students.

A First Course in Stochastic Processes focuses on several principal areas of stochastic processes and the diversity of applications of stochastic processes, including Markov chains, Brownian motion, and Poisson processes. The publication first takes a look at the elements of stochastic processes, Markov chains, and the basic limit theorem of Markov chains and applications. Discussions focus on criteria for recurrence, absorption probabilities, discrete renewal equation, classification of states of a Markov chain, and review of basic terminologies and properties of random variables and distribution functions. The text then examines algebraic methods in Markov chains and ratio theorems of transition probabilities and applications. The manuscript elaborates on the sums of independent random variables as a Markov chain, classical examples of continuous time Markov chains, and continuous time Markov chains. Topics include differentiability properties of transition probabilities, birth and death processes with absorbing states, general pure birth processes and Poisson processes, and recurrence properties of sums of independent random variables. The book then ponders on Brownian motion, compounding stochastic processes, and deterministic and stochastic genetic and ecological processes. The publication is a valuable source of information for readers interested in stochastic processes.

An Introduction to Stochastic Modeling provides information pertinent to the standard concepts and methods of stochastic modeling. This book presents the rich diversity of applications of stochastic processes in the sciences. Organized into nine chapters, this book begins with an overview of diverse types of stochastic models, which predicts a set of possible outcomes weighed by their likelihoods or probabilities. This text then provides exercises in the applications of simple stochastic analysis to appropriate problems. Other chapters consider the study of general functions of independent, identically distributed, nonnegative random variables representing the successive intervals between renewals. This book discusses as well the numerous examples of Markov branching processes that arise naturally in various scientific disciplines. The final chapter deals with queueing models, which aid the design process by predicting system performance. This book is a valuable resource for students of engineering and management science. Engineers will also find this book useful.