Ebook: Stochastic Analysis, Control, Optimization and Applications: A Volume in Honor of W.H. Fleming

In view of Professor Wendell Fleming's many fundamental contributions, his profound influence on the mathematical and systems theory communi­ ties, his service to the profession, and his dedication to mathematics, we have invited a number of leading experts in the fields of control, optimiza­ tion, and stochastic systems to contribute to this volume in his honor on the occasion of his 70th birthday. These papers focus on various aspects of stochastic analysis, control theory and optimization, and applications. They include authoritative expositions and surveys as well as research papers on recent and important issues. The papers are grouped according to the following four major themes: (1) large deviations, risk sensitive and Hoc control, (2) partial differential equations and viscosity solutions, (3) stochastic control, filtering and parameter esti­ mation, and (4) mathematical finance and other applications. We express our deep gratitude to all of the authors for their invaluable contributions, and to the referees for their careful and timely reviews. We thank Harold Kushner for having graciously agreed to undertake the task of writing the foreword. Particular thanks go to H. Thomas Banks for his help, advice and suggestions during the entire preparation process, as well as for the generous support of the Center for Research in Scientific Computation. The assistance from the Birkhauser professional staff is also greatly appreciated.

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Content:
Front Matter....Pages i-xxxii
Front Matter....Pages N1-N1
Representations for Functional of Hilbert Space Valued Diffusions....Pages 1-20
Risk-Sensitive, Minimax, and Mixed Risk-Neutral / Minimax Control of Markov Decision Processes....Pages 21-40
Partially Observed Control Problems with Multiplicative Cost....Pages 41-55
Nonlinear Semigroups for Partially Observed Risk-Sensitive Control and Minimax Games....Pages 57-73
Nonlinear, Dissipative, Infinite Dimensional Systems....Pages 75-93
Singular Limits of Bellman Equations of Ergodic Type Related to Risk-Sensitive Control....Pages 95-114
Game Approach to Risk Sensitive Control for Stochastic Evolution Systems....Pages 115-134
On the Solutions of the Equation Arising from the Singular Limit of Some Eigen Problems....Pages 135-150
Front Matter....Pages 151-170
Singularities of Semiconcave Functions in Banach Spaces....Pages N2-N2
Invariant Sets for Controlled Degenerate Diffusions: A Viscosity Solutions Approach....Pages 171-190
Remarks on the Dirichlet Problem for Quasilinear Elliptic and Parabolic Equations....Pages 191-208
A Generalized Hamilton—Jacobi—Bellman Equation for Deterministic Optimal Control Problems....Pages 209-222
Regular Solutions of Stochastic Burgers Equation....Pages 223-235
Piecewise-Deterministic Processes and Viscosity Solutions....Pages 237-247
Mathematical Approaches to the Problem of Noise-Induced Exit....Pages 249-268
An Approximation Scheme for Evolutive Hamilton-Jacobi Equations....Pages 269-287
Homogenization of the Cauchy Problem for Hamilton-Jacobi Equations....Pages 289-303
The Critical Exponent for a Stochastic PDE to Hit Zero....Pages 305-324
Front Matter....Pages 325-338
Robustness of Zakai’s Equation via Feynman-Kac Representations....Pages N3-N3
Front Matter....Pages 339-352
Estimation of Probability Distributions for Individual Parameters Using Aggregate Population Data....Pages N3-N3
Solvable Infinite Time Horizon Stochastic Control Problems in Noncompact Symmetric Spaces....Pages 353-371
Exact Finite Dimensional Filters for Exponential Functional of the State....Pages 373-389
A Lyapunov Theory of Nonlinear Observers....Pages 391-408
Existence of Optimal Controls for Variance Control....Pages 409-420
On Optimal Ergodic Control of Diffusions with Jumps....Pages 421-437
Markov Marginal Problems and Their Applications to Markov Optimal Control....Pages 439-456
Entropy Inequalities and Entropy Dynamics in Nonlinear Filtering of Diffusion Processes....Pages 457-476
Identification for Linear Stochastic Distributed Parameter Systems with Boundary/Point Control....Pages 477-496
Monte Carlo Estimation of Diffusion Distributions at Inter-sampling Times....Pages 497-504
Front Matter....Pages 505-520
Option Pricing in a Market with Frictions....Pages N4-N4
Pathwise Comparison of Arithmetric Brownian Motions and Log-normal Processes....Pages 521-540
Critical Power for Asymptotic Connectivity in Wireless Networks....Pages 541-546
Pricing Models with Transaction Fees....Pages 547-566
A Verification Theorem in General Equilibrium Model of Asset Prices....Pages 567-584
Optimal Portfolio Management with Partial Observations and Power Utility Function....Pages 585-604
Hierarchical Production Controls for a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality....Pages 605-619
....Pages 621-637