1st Edition

Real and Stochastic AnalysisRecent Advances



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ISBN 9780849380785
Published March 6, 1997 by CRC Press
416 Pages

USD $195.00

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Book Description

Real and Stochastic Analysis: Recent Advances presents a carefully edited collection of research articles written by research mathematicians and highlighting advances in RSA. A balanced blend of both theory and applications, this book covers six aspects of stochastic analysis in depth and detail.
The first chapters cover the state of the art in tracers analysis, stochastic modeling as it applies to AIDS epidemiology, and the current state of higher order SDEs. Subsequent chapters present a simple approach to Gaussian dichotomy, an overview of harmonizable processes, and stochastic Fubini and Green theorems. Common to all the chapters, the employment of functional analytic methods creates a unified approach. Each chapter includes detailed proofs.
Throughout the book, a substantial amount of new material is presented, much of it for the first time. This forward-looking work presents current accounts of important areas of research, evaluates recent advances, and identifies research frontiers and new challenges.

Table of Contents

Introduction and Overview, M.M. Rao
Transport Properties of Gaussian Velocity Fields, R.A. Carmona
Introduction
Gaussian Velocity Fields
Infinite-Dimensional Ornstein-Uhlenbeck Processes
Transport Problems
Numerical Simulations
The Case of White Velocity Fields
Open Mathematical Problems
Stochastic Flows and SPDEs
Bibliography
Planar Stochastic Integration Relative to Quasimartingales, M.L. Green
Introduction
The Bochner Bounding Measure for V-Quasimartingales
Line Integrals
The Mixed Integral
The Double Integral
The JX-Measure
A Stochastic Green Theorem
Bibliography
Probability Metrics and Limit Theorems in AIDS Epidemiology, S.T. Rachev, V. Haynatzka, and G. Haynatzki
Introduction
The Monge-Kantorovitch Problem and Probability Metrics
Ideal Metrics
Spread of AIDS Among Drug Users and Probability Metrics
The Spread of AIDS Among Interactive Transmission Groups
Bibliography
Higher Order Stochastic Differential Equations, M.M. Rao
Introduction
Stochastic Integrals and Boundedness Principles
Linear Stochastic Differential Equations
Higher Order Nonlinear Equations
Infinitesimal Characteristics of Solutions
Refined Analysis with Brownian Noise
Operator Representation of the V-Process
Sample Path Behavior for Large Time
Aspects of Stochastic Flows
Multiparameter Analogs and SPDEs
Bibliography
Some Aspects of Harmonizable Processes and Fields, R.J. Swift
Introduction
Preliminaries
Part I: Second Order Nonstationary Processes Including the Harmonizable Class
Part II: Some Classes of Harmonizable Random Fields
Bibliography
On Singularity and Equivalence of Gaussian Measures, N. Vakhania and V. Tarieladze
Definitions and Auxiliary Results
Kakutani's Theorem
Gaussian Measures on R
General Gaussian Measures
The Case of Topological Vector Spaces
Bibliography
Index

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