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

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