Stochastic Analysis - 1st Edition - ISBN: 9780124810051, 9781483218700

Stochastic Analysis

1st Edition

Liber Amicorum for Moshe Zakai

Editors: Eddy Mayer-Wolf Ely Merzbach Adam Shwartz
eBook ISBN: 9781483218700
Imprint: Academic Press
Published Date: 28th April 1991
Page Count: 552
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Description

Stochastic Analysis: Liber Amicorum for Moshe Zakai focuses on stochastic differential equations, nonlinear filtering, two-parameter martingales, Wiener space analysis, and related topics.

The selection first ponders on conformally invariant and reflection positive random fields in two dimensions; real time architectures for the Zakai equation and applications; and quadratic approximation by linear systems controlled from partial observations. Discussions focus on predicted miss, review of basic sequential detection problems, multigrid algorithms for the Zakai equation, invariant test functions and regularity, and reflection positivity. The text then takes a look at a model of stochastic differential equation in Hubert spaces applicable to Navier Stokes equation in dimension 2; wavelets as attractors of random dynamical systems; and Markov properties for certain random fields.

The publication examines the anatomy of a low-noise jump filter, nonlinear filtering with small observation noise, and closed form characteristic functions for certain random variables related to Brownian motion. Topics include derivation of characteristic functions for the examples, proof of the theorem, sequential quadratic variation test, asymptotic optimal filters, mean decision time, and asymptotic optimal filters.

The selection is a valuable reference for researchers interested in stochastic analysis.

Table of Contents


Invited Speakers to the Conference in Honor of Moshe Zakai are Denoted by a star*

Preface

Foreword

Publications by Moshe Zakai

Conformally Invariant and Reflection Positive Random Fields in Two Dimensions

Real Time Architectures for the Zakai Equation and Applications

Quadratic Approximation by Linear Systems Controlled from Partial Observations

A Model of Stochastic Differential Equation in Hilbert Spaces Applicable to Navier Stokes Equation in Dimension 2

Wavelets as Attractors of Random Dynamical Systems

Markov Properties for Certain Random Fields

The Anatomy of a Low-Noise Jump Filter: Part I

On the Value of Information in Controlled Diffusion Processes

Orthogonal Martingale Representation

Nonlinear Filtering with Small Observation Noise: Piecewise Monotone Observations

Closed Form Characteristic Functions for Certain Random Variables Related to Brownian Motion

Adaptedness and Existence of Occupation Densities for Stochastic Integral Processes in the Second Wiener Chaos

A Skeletal Theory of Filtering

Equilibrium in a Simplified Dynamic, Stochastic Economy with Heterogeneous Agents

Feynman-Kac Formula for a Degenerate Planar Diffusion and an Application in Stochastic Control

On the Interior Smoothness of Harmonic Functions for Degenerate Diffusion Processes

The Stability and Approximation Problems in Nonlinear Filtering Theory

Wong-Zakai Corrections, Random Evolutions, and Simulation Schemes for SDE's

Nonlinear Filtering for Singularly Perturbed Systems

Smooth σ-Fields

Composition of Large Deviation Principles and Applications

Nonlinear Transformations of the Wiener Measure and Applications

Finite Dimensional Approximate Filters in the Case of High Signal-To-Noise Ratio

A Simple Proof of Uniqueness for Kushner and Zakai Equations

Itô-Wiener Expansions of Holomorphic Functions on the Complex Wiener Space

Limits of the Wong-Zakai Type with a Modified Drift Term

Donsker's δ-Functions in the Malliavin Calculus

Implementing Boltzmann Machines

Infinite Dimensionality Results for MAP Estimation

Details

No. of pages:
552
Language:
English
Copyright:
© Academic Press 1991
Published:
Imprint:
Academic Press
eBook ISBN:
9781483218700

About the Editor

Eddy Mayer-Wolf

Ely Merzbach

Adam Shwartz

Ratings and Reviews