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Theory of Stochastic Processes

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Cover of 'Theory of Stochastic Processes'

Table of Contents

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    Book Overview
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    Chapter 1 Definition of stochastic process. Cylinder σ-algebra, finite-dimensional distributions, the Kolmogorov theorem
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    Chapter 2 Characteristics of a stochastic process. Mean and covariance functions. Characteristic functions
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    Chapter 3 Trajectories. Modifications. Filtrations
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    Chapter 4 Continuity. Differentiability. Integrability
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    Chapter 5 Stochastic processes with independent increments. Wiener and Poisson processes. Poisson point measures
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    Chapter 6 Gaussian processes
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    Chapter 7 Martingales and related processes in discrete and continuous time. Stopping times
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    Chapter 8 Stationary discrete- and continuous-time processes. Stochastic integral over measure with orthogonal values
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    Chapter 9 Prediction and interpolation
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    Chapter 10 Markov chains: Discrete and continuous time
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    Chapter 11 Renewal theory. Queueing theory
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    Chapter 12 Markov and diffusion processes
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    Chapter 13 Itô stochastic integral. Itô formula. Tanaka formula
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    Chapter 14 Stochastic differential equations
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    Chapter 15 Optimal stopping of random sequences and processes
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    Chapter 16 Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems
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    Chapter 17 Statistics of stochastic processes
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    Chapter 18 Stochastic processes in financial mathematics (discrete time)
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    Chapter 19 Stochastic processes in financial mathematics (continuous time)
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    Chapter 20 Basic functionals of the risk theory
Attention for Chapter 16: Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems
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Chapter title
Measures in a functional spaces. Weak convergence, probability metrics. Functional limit theorems
Chapter number 16
Book title
Theory of Stochastic Processes
Published by
Springer, New York, NY, January 2010
DOI 10.1007/978-0-387-87862-1_16
Book ISBNs
978-0-387-87861-4, 978-0-387-87862-1
Authors

Dmytro Gusak, Alexander Kukush, Alexey Kulik, Yuliya Mishura, Andrey Pilipenko

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