Stochastic Processes Lectures Given at Aarhus University

Name: Stochastic Processes Lectures Given at Aarhus University
Availability: InStock
ISBN: 9783540204824

ISBN-10: 3540204822

ISBN-13: 9783540204824

Edition: 2004

Authors: Ole E. Barndorff-Nielsen, Ken-iti Sato, Kiyosi Ito

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Description:

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 Lvy-It decomposition, in a form close to It'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…

Book details

List price: $84.99
Copyright year: 2004
Publisher: Springer Berlin / Heidelberg
Publication date: 3/12/2004
Binding: Hardcover
Pages: 236
Size: 6.10" wide x 9.25" long x 0.30" tall
Weight: 2.574




Additive processes (processes with independent increments)


Definitions


Decomposition of additive processes


The Levy modification of additive processes continuous in probability


Elementary Levy processes


Fundamental lemma


Structure of sample functions of Levy processes (a)


Structure of sample functions of Levy processes (b)


Three components of Levy processes


Random point measures


Homogeneous additive processes and homogeneous Levy processes


Levy processes with increasing paths


Stable processes



Markov processes


Transition probabilities and transition operators on compact metrizable spaces


Summary of the Hille-Yosida theory of semi-groups


Transition semi-group


Probability law of the path


Markov property


The a-algebras B, B[subscript 1] and B(S)


Strong Markov property


An inequality of Kolmogorov type and its application


Hitting times of closed sets


Dynkin's formula


Markov processes in generalized sense


Examples


Markov processes with a countable state space


Fine topology


Generator in generalized sense


The Kac semi-group and its application to the Arcsine law


Markov processes and potential theory


Brownian motion and the Dirichlet problem