Stochastic Analysis

Stochastic Analysis

Liber Amicorum for Moshe Zakai

1st Edition - April 28, 1991

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  • Editors: Eddy Mayer-Wolf, Ely Merzbach, Adam Shwartz
  • eBook ISBN: 9781483218700

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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

Product details

  • No. of pages: 552
  • Language: English
  • Copyright: © Academic Press 1991
  • Published: April 28, 1991
  • Imprint: Academic Press
  • eBook ISBN: 9781483218700

About the Editors

Eddy Mayer-Wolf

Ely Merzbach

Adam Shwartz

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