Stochastic Analysis, Control, Optimization and Applications

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

• ISBN13: 9780817640781
• ISBN10: 0817640789
• Format: Hardcover
• Copyright: 1999-05-01
• Publisher: Birkhauser

Summary

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.

Table of Contents

Preface	xi
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	1	(20)
A. Budhiraja
P. Dupuis
Risk-Sensitive, Minimax, and Mixed Risk-Neutral/Minimax Control of Markov Decision Processes	21	(20)
S.P. Coraluppi
S.I. Marcus
Partially Observed Control Problems with Multiplicative Cost	41	(16)
D. Hernandez-Hernandez
Nonlinear Semigroups for Partially Observed Risk-Sensitive Control and Minimax Games	57	(18)
M.R. James
Nonlinear, Dissipative, Infinite Dimensional Systems	75	(20)
M. Kocan
P. Soravia
Singular Limits of Bellman Equations of Ergodic Type Related to Risk-Sensitive Control	95	(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