Stochastic Analysis, Control, Optimization and Applications

, by McEneaney, William M.; Yin, G. George; Zhang, Qing

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ISBN: 9780817640781 | 0817640789
Cover: Hardcover
Copyright: 5/1/1999

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This volume was written in honor of Wendell H. Fleming, a mathematician who has made fundamental contributions in the fields of calculus of variations, geometric measure theory, differential games, stochastic control theory, and population genetics. This book includes authoritative expositions and surveys focusing on the key recent developments and results in stochastic analysis, control theory and optimization, as well as their applications.

Preface

Foreword

xiii

W.H. Fleming's Curriculum Vitae

xvii

Contributors and Addresses

xxvii

PART I. LARGE DEVIATIONS, RISK SENSITIVE AND H∞ CONTROL

Representations for Functionals of Hilbert Space Valued Diffusions

(20)

A. Budhiraja

P. Dupuis

Risk-Sensitive, Minimax, and Mixed Risk-Neutral/Minimax Control of Markov Decision Processes

(20)

S.P. Coraluppi

S.I. Marcus

Partially Observed Control Problems with Multiplicative Cost

(16)

D. Hernandez-Hernandez

Nonlinear Semigroups for Partially Observed Risk-Sensitive Control and Minimax Games

(18)

M.R. James

Nonlinear, Dissipative, Infinite Dimensional Systems

(20)

M. Kocan

P. Soravia

Singular Limits of Bellman Equations of Ergodic Type Related to Risk-Sensitive Control

(20)

H. Nagai

Game Approach to Risk Sensitive Control for Stochastic Evolution Systems

115

(20)

M. Nisio

On the Solutions of the Equation Arising from the Singular Limit of Some Eigen Problems

135

(16)

S.-J. Sheu

A.D. Wentzell

Nonlinear H∞ Controller Design via Viscosity Supersolutions of the Isaacs Equation

151

(20)

M. Xiao

T. Basar

PART II. PARTIAL DIFFERENTIAL EQUATIONS AND VISCOSITY SOLUTIONS

Singularities of Semiconcave Functions in Banach Spaces

171

(20)

P. Albano

P. Cannarsa

Invariant Sets for Controlled Degenerate Diffusions: A Viscosity Solutions Approach

191

(18)

M. Bardi

P. Goatin

Remarks on the Dirichlet Problem for Quasilinear Elliptic and Parabolic Equations

209

(14)

G. Barles

E. Rouy

P.E. Souganidis

A Generalized Hamilton-Jacobi-Bellman Equation for Deterministic Optimal Control Problems

223

(14)

L.D. Berkovitz

Regular Solutions of Stochastic Burgers Equation

237

(12)

P.L. Chow

Piecewise-Deterministic Processes and Viscosity Solutions

249

(20)

M.H.A. Davis

M. Farid

Mathematical Approaches to the Problem of Noise-Induced Exit

269

(20)

M.V. Day

An Approximation Scheme for Evolutive Hamilton-Jacobi Equations

289

(16)

M. Falcone

T. Giorgi

Homogenization of the Cauchy Problem for Hamilton-Jacobi Equations

305

(20)

H. Ishii

The Critical Exponent for a Stochastic PDE to Hit Zero

325

(14)

C. Mueller

E. Pardoux

PART III. STOCHASTIC CONTROL, FILTERING AND PARAMETER ESTIMATION

Robustness of Zakai's Equation via Feynman-Kac Representations

339

(14)

R. Atar

F. Viens

O. Zeitouni

Estimation of Probability Distributions for Individual Parameters Using Aggregate Population Data

353

(20)

H.T. Banks

B.G. Fitzpatrick

L.K. Potter

Y. Zhang

Solvable Infinite Time Horizon Stochastic Control Problems in Noncompact Symmetric Spaces

373

(18)

T.E. Duncan

Exact Finite Dimensional Filters for Exponential Functionals of the State

391

(18)

R.J. Elliott

V. Krishnamurthy

A Lyapunov Theory of Nonlinear Observers

409

(12)

A.J. Krener

Existence of Optimal Controls for Variance Control

421

(18)

H.J. Kushner

On Optimal Ergodic Control of Diffusions with Jumps

439

(18)

J.-L. Menaldi

M. Robin

Markov Marginal Problems and Their Applications to Markov Optimal Control

457

(20)

T. Mikami

Entropy Inequalities and Entropy Dynamics in Nonlinear Filtering of Diffusion Processes

477

(20)

D. Ocone

Identification for Linear Stochastic Distributed Parameter Systems with Boundary/Point Control

497

(8)

B. Pasik-Duncan

Monte Carlo Estimation of Diffusion Distributions at Inter-sampling Times

505

(16)

C.J. Wypasek

J.V. Butera

B.G. Fitzpatrick

PART IV. MATHEMATICAL FINANCE AND OTHER APPLICATIONS

Option Pricing in a Market with Frictions

521

(20)

A. Bensoussan

H. Julien

Pathwise Comparison of Arithmetic Brownian Motions and Log-normal Processes

541

(6)

G. Ferreyra

P. Sundar

Critical Power for Asymptotic Connectivity in Wireless Networks

547

(20)

P. Gupta

P.R. Kumar

Pricing Models with Transaction Fees

567

(18)

J.E. Hodder

T. Zariphopoulou

A Verification Theorem in General Equilibrium Model of Asset Prices

585

(20)

C.-F. Huang

M. Taksar

S.H. Zhu

Optimal Portfolio Management with Partial Observations and Power Utility Function

605

(16)

R. Rishel

Hierarchical Production Controls for a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality

621

S.P. Sethi

H. Zhang

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Stochastic Analysis, Control, Optimization and Applications

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