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Stochastic Processes Lectures Given at Aarhus University

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ISBN-10: 3540204822

ISBN-13: 9783540204824

Edition: 2004

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

List price: $84.99
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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…    
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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
Language: English

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