Stochastic Processes

ISBN-13: 9780471523697 / Angielski / Miękka / 1991 / 664 str.

J. L. Doob; Joseph L. Doob;Doob

Opis

The theory of stochastic processes has developed so much in the last two decades that the need for a systematic account of the subject has been felt, particularly by students and instructors of probability. This book features a supplement which provides a treatment of the various aspects of measure theory. A chapter on the specialized problem of prediction theory has also been included, and references to the literature and historical remarks have been collected in the appendix.

Spis treści

Introduction and Probability Background.

Definition of a Stochastic Process––Principal Classes.

Processes with Mutually Independent Random Variables.

Processes with Mutually Uncorrelated or Orthogonal Random Variables.

Markov Processes––Discrete Parameter.

Markov Processes––Continuous Parameter.

Martingales.

Processes with Independent Increments.

Processes with Orthogonal Increments.

Stationary Processes––Discrete Parameter.

Stationary Processes––Continuous Parameter.

Linear Least Squares Prediction––Stationary (Wide Sense) Processes.

Supplement.

Appendix.

Bibliography.

Index.

Blurb

The Wiley Classics Library consists of selected books originally published by John Wiley & Sons that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes With Applications to the Natural Sciences R. W. Carter Simple Groups of Lie Type Richard Courant Differential and Integral Calculus. Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II Harold S.M. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory With Applications to Finite Groups and Orders, Volume 1 W. Edwards Darning Sample Design in Business Research Amos deShalit & Herman Feshbach Theoretical Nuclear Physics, Volume I–Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford, Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford, Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory – Self Adjoint Operators in Hilbert Space Nelson Dunford, Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Peter Henrici Applied and Computational Complex Analysis, Volume I – Power Series–Integration–Conformal Mapping–Location of Zeros Peter Hilton, Yel–Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation P. M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory Volume I – Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory Volume II – Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III – Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry