Stochastic Analysis, Control, Optimization and Applications -

. .

Résumé :
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.

Sommaire:
I. Large Deviations, Risk Sensitive And H?, Control.- 1. Representations for Functionals of Hilbert Space Valued Diffusions.- 2. Risk-Sensitive, Minimax, and Mixed Risk-Neutral/Minimax Control of Markov Decision Processes.- 3. Partially Observed Control Problems with Multiplicative Cost.- 4. Nonlinear Semigroups for Partially Observed Risk-Sensitive Control and Minimax Games.- 5. Nonlinear, Dissipative, Infinite Dimensional Systems.- 6. Singular Limits of Bellman Equations of Ergodic Type Related to Risk-Sensitive Control.- 7. Game Approach to Risk Sensitive Control for Stochastic Evolution Systems.- 8. On the Solutions of the Equation Arising from the Singular Limit of Some Eigen Problems.- 9. Nonlinear H? Controller Design via Viscosity Supersolutions of the Isaacs Equation.- II. Partial Differential Equations and Viscosity Solutions.- 10. Singularities of Semiconcave Functions in Banach Spaces.- 11. Invariant Sets for Controlled Degenerate Diffusions: A Viscosity Solutions Approach.- 12. Remarks on the Dirichlet Problem for Quasilinear Elliptic and Parabolic Equations.- 13. A Generalized Hamilton-Jacobi-Bellman Equation for Deterministic Optimal Control Problems.- 14. Regular Solutions of Stochastic Burgers Equation.- 15. Piecewise-Deterministic Processes and Viscosity Solutions.- 16. Mathematical Approaches to the Problem of Noise-Induced Exit.- 17. An Approximation Scheme for Evolutive Hamilton-Jacobi Equations.- 18. Homogenization of the Cauchy Problem for Hamilton-Jacobi Equations.- 19. The Critical Exponent for a Stochastic PDE to Hit Zero.- III. Stochastic Control, Filtering and Parameter Estimation.- 20. Robustness of Zakai's Equation via Feynman-Kac Representations.- 21. Estimation of Probability Distributions for Individual Parameters Using AggregatePopulation Data.- 22. Solvable Infinite Time Horizon Stochastic Control Problems in Noncompact Symmetric Spaces.- 23. Exact Finite Dimensional Filters for Exponential Functionals of the State.- 24. A Lyapunov Theory of Nonlinear Observers.- 25. Existence of Optimal Controls for Variance Control.- 26. On Optimal Ergodic Control of Diffusions with Jumps.- 27. Markov Marginal Problems and Their Applications to Markov Optimal Control.- 28. Entropy Inequalities and Entropy Dynamics in Nonlinear Filtering of Diffusion Processes.- 29. Identification for Linear Stochastic Distributed Parameter Systems with Boundary/Point Control.- 30. Monte Carlo Estimation of Diffusion Distributions at Inter-sampling Times.- IV. Mathematical Finance and Other Applications.- 31. Option Pricing in a Market with Frictions.- 32. Pathwise Comparison of Arithmetic Brownian Motions and Log-normal Processes.- 33. Critical Power for Asymptotic Connectivity in Wireless Networks.- 34. Pricing Models with Transaction Fees.- 35. A Verification Theorem in General Equilibrium Model of Asset Prices.- 36. Optimal Portfolio Management with Partial Observations and Power Utility function.- 37. Hierarchical Production Controls for a Stochastic Manufacturing System with Long-Run Average Cost: Asymptotic Optimality.