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6 produkter
6 produkter
Del 68 - Cambridge Studies in Advanced Mathematics
Lévy Processes and Infinitely Divisible Distributions
Inbunden, Engelska, 1999
1 850 kr
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Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer.
Del 68 - Cambridge Studies in Advanced Mathematics
Lévy Processes and Infinitely Divisible Distributions
Häftad, Engelska, 2013
901 kr
Skickas inom 7-10 vardagar
Lévy processes are rich mathematical objects and constitute perhaps the most basic class of stochastic processes with a continuous time parameter. This book is intended to provide the reader with comprehensive basic knowledge of Lévy processes, and at the same time serve as an introduction to stochastic processes in general. No specialist knowledge is assumed and proofs are given in detail. Systematic study is made of stable and semi-stable processes, and the author gives special emphasis to the correspondence between Lévy processes and infinitely divisible distributions. All serious students of random phenomena will find that this book has much to offer. Now in paperback, this corrected edition contains a brand new supplement discussing relevant developments in the area since the book's initial publication.
Topics in Infinitely Divisible Distributions and Lévy Processes, Revised Edition
Häftad, Engelska, 2019
641 kr
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This book deals with topics in the area of Lévy processes and infinitely divisible distributions such as Ornstein-Uhlenbeck type processes, selfsimilar additive processes and multivariate subordination.
800 kr
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This is a readily accessible introduction to the theory of stochastic processes with emphasis on processes with independent increments and Markov processes. After preliminaries on infinitely divisible distributions and martingales, Chapter 1 gives a thorough treatment of the decomposition of paths of processes with independent increments, today called the Levy-Ito decomposition, in a form close to Ito's original paper from 1942. Chapter 2 contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. Two separate Sections present about 70 exercises and their complete solutions. The text and exercises are carefully edited and footnoted, while retaining the style of the original lecture notes from Aarhus University.
641 kr
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The volume Stochastic Processes by K. Itö was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lévy-It ö decomposition of additive processes. Encouraged by Professor It ó we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ran dom variables are treated using the dispersion as a main tooI. Lévy's form of characteristic functions of infinitely divisible distributions and basic proper ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure the orem describes the decomposition of sample functions of additive processes, known today as the Lévy-Itó decomposition. This is thoroughly treated, as suming no continuity property in time, in a form close to the original 1942 paper of Itó, which gave rigorous expression to Lévy's intuitive understanding of path behavior.
Del 2001 - Lecture Notes in Mathematics
Lévy Matters I
Recent Progress in Theory and Applications: Foundations, Trees and Numerical Issues in Finance
Häftad, Engelska, 2010
536 kr
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Over the past 10-15 years, we have seen a revival of general Levy ' processes theory as well as a burst of new applications. In the past, Brownian motion or the Poisson process have been considered as appropriate models for most applications. Nowadays, the need for more realistic modelling of irregular behaviour of phen- ena in nature and society like jumps, bursts, and extremeshas led to a renaissance of the theory of general Levy ' processes. Theoretical and applied researchers in elds asdiverseas quantumtheory,statistical physics,meteorology,seismology,statistics, insurance, nance, and telecommunication have realised the enormous exibility of Lev ' y models in modelling jumps, tails, dependence and sample path behaviour. L' evy processes or Levy ' driven processes feature slow or rapid structural breaks, extremal behaviour, clustering, and clumping of points. Toolsandtechniquesfromrelatedbut disctinct mathematical elds, such as point processes, stochastic integration,probability theory in abstract spaces, and differ- tial geometry, have contributed to a better understanding of Le 'vy jump processes.As in many other elds, the enormous power of modern computers has also changed the view of Levy ' processes. Simulation methods for paths of Levy ' p- cesses and realisations of their functionals have been developed. Monte Carlo simulation makes it possible to determine the distribution of functionals of sample paths of Levy ' processes to a high level of accuracy.