Stationary Stochastic Processes

Takeyuki Hida

Book

Stationary Stochastic Processes

Takeyuki Hida

Language: English

Published/Copyright: 1970

Published by

View more publications by Princeton University Press

To Publisher Page

This book is in the series

Mathematical Notes

This book is in the series

Volume 8 | Monographs in Population Biology

This book is in the series

Princeton Legacy Library

About this book

Encompassing both introductory and more advanced research material, these notes deal with the author's contributions to stochastic processes and focus on Brownian motion processes and its derivative white noise.

Originally published in 1970.

The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Topics

Mathematics Probability and Statistics

Frontmatter Publicly Available Download PDF	i
Preface Requires Authentication Unlicensed Licensed	iii
Contents Publicly Available Download PDF	iv
0. Introduction Requires Authentication Unlicensed Licensed	1
1. Background Requires Authentication Unlicensed Licensed	3
2. Brownian motion Requires Authentication Unlicensed Licensed	14
3. Additive processes Requires Authentication Unlicensed Licensed	31
4. Stationary processes Requires Authentication Unlicensed Licensed	62
5. Gaussian processes Requires Authentication Unlicensed Licensed	86
6. Hilbert space(L²) arising from white noise Requires Authentication Unlicensed Licensed	94
7. FLow of the Brownian motion. Requires Authentication Unlicensed Licensed	106
8. Infinite dimensional rotation group Requires Authentication Unlicensed Licensed	113
9. Fourier Analysis on (L² ) , motion group and Laplacian Requires Authentication Unlicensed Licensed	120
10. Applications Requires Authentication Unlicensed Licensed	135
11. Generalized White Noise Requires Authentication Unlicensed Licensed	147
Appendix Requires Authentication Unlicensed Licensed	163

Publishing information

Pages and Images/Illustrations in book

eBook published on:

March 8, 2015

eBook ISBN:

9781400868575

Pages and Images/Illustrations in book

Main content:

174

https://doi.org/10.1515/9781400868575

eBook ISBN: 9781400868575

Keywords for this book

Stationary process; White noise; Gaussian process; Theorem; Brownian motion; Polynomial; Parameter; Subgroup; Poisson point process; Compound Poisson process; Exponential function; Unitary operator; Stochastic process; Existential quantification; Probability measure; One-parameter group; Hilbert space; Characteristic function (probability theory); Infinitesimal generator (stochastic processes); Hermite polynomials; Stable process; Probability distribution; Random variable; Lebesgue measure; Self-adjoint operator; Eigenfunction; Finite difference; Probability space; Monotonic function; Linear combination; Derivative; Reproducing kernel Hilbert space; Characteristic exponent; Nuclear space; Function space; Semigroup; Fourier series; Integral equation; Equation; Computation; Normal distribution; Bounded variation; Summation; Langevin equation; Independence (probability theory); Normal subgroup; Radon–Nikodym theorem; Dirac delta function; Cyclic subspace; Continuous function; Discrete spectrum; Symmetrization; Indicator function; Degrees of freedom (statistics); Continuous function (set theory); Covariance function; Orthogonalization; Limit superior and limit inferior; Bochner's theorem; Self-adjoint; Joint probability distribution; Bounded operator; Exponential distribution; Stochastic; Independent and identically distributed random variables; Linear function; Cylinder set; Continuous linear operator; Zero element; Unitary transformation

Audience(s) for this book

College/higher education;Professional and scholarly;

Stationary Stochastic Processes

Overview

About this book

Topics

Table of contents

Bibliographic data