Ebook: Stochastic Differential Systems, Stochastic Control Theory and Applications

This IMA Volume in Mathematics and its Applications STOCHASTIC DIFFERENTIAL SYSTEMS, STOCHASTIC CONTROL THEORY AND APPLICATIONS is the proceedings of a workshop which was an integral part of the 1986-87 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS. We are grateful to the Scientific Committee: Daniel Stroock (Chairman) WendeIl Flerning Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We es­ pecially thank WendeIl Fleming and Pierre-Louis Lions for organizing an interesting and productive workshop in an area in which mathematics is beginning to make significant contributions to real-world problems. George R. Seil Hans Weinberger PREFACE This volume is the Proceedings of a Workshop on Stochastic Differential Systems, Stochastic Control Theory, and Applications held at IMA June 9-19,1986. The Workshop Program Commit­ tee consisted of W.H. Fleming and P.-L. Lions (co-chairmen), J. Baras, B. Hajek, J.M. Harrison, and H. Sussmann. The Workshop emphasized topics in the following four areas. (1) Mathematical theory of stochastic differential systems, stochastic control and nonlinear filtering for Markov diffusion processes. Connections with partial differential equations. (2) Applications of stochastic differential system theory, in engineering and management sci­ ence. Adaptive control of Markov processes. Advanced computational methods in stochas­ tic control and nonlinear filtering. (3) Stochastic scheduling, queueing networks, and related topics. Flow control, multiarm bandit problems, applications to problems of computer networks and scheduling of complex manufacturing operations.

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This volume has resulted from an IMA workshop that sought to provide a mix of topics from both traditional areas of stochastic control theory and newer areas of application. The papers represent a diversity of approaches and points of view and emphasize to different extents the underlying mathematical theory, or modeling issues or questions of computational implementation.

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This volume has resulted from an IMA workshop that sought to provide a mix of topics from both traditional areas of stochastic control theory and newer areas of application. The papers represent a diversity of approaches and points of view and emphasize to different extents the underlying mathematical theory, or modeling issues or questions of computational implementation.
Content:
Front Matter....Pages i-xiii
Optimality of “full bang to reduce predicted miss” for some partially observed stochastic control problems....Pages 1-15
On Some Approximation Techniques in Non Linear Filtering....Pages 17-31
Applications of Homogenization Theory to the Control of Flexible Structures....Pages 33-55
Control of Markov Chains with Long-Run Average Cost Criterion....Pages 57-77
Automatic Study in Stochastic Control....Pages 79-86
Some Results on Kolmogoroff Equations for Infinite Dimensional Stochastic Systems....Pages 87-97
Hamilton-Jacobi Equations with Constraints....Pages 99-106
An Approximate Minimum Principle for a Partially Observed Markov Chain....Pages 107-117
Generalized Solutions in the Optimal Control of Diffusions....Pages 119-127
Consistency of Maximum Likelihood and Pseudo-Likelihood Estimators for Gibbs Distributions....Pages 129-145
Brownian Models of Queueing Networks with Heterogeneous Customer Populations....Pages 147-186
Non-Linear Filtering — The Degenerate Case....Pages 187-203
The Asymptotic Behaviour of the Maximum Likelihood Estimates for a Class of Diffusion Processes....Pages 205-213
The Filtering Problem for Infinite Dimensional Stochastic Processes....Pages 215-223
Stochastic Control Under Finite-Fuel Constraints....Pages 225-240
Recent Advances in the Theory of Stochastic Adaptive Control....Pages 241-254
Almost Optimal Controls for Wideband Noise Driven Systems....Pages 255-273
Asymptotic Solutions of Bandit Problems....Pages 275-292
Viscosity Solutions of Second-Order Equations, Stochastic Control and Stochastic Differential Games....Pages 293-309
On the Memory Length of the Optimal Nonlinear Filter....Pages 311-322
Implementation Issues for Markov Decision Processes....Pages 323-337
Navigating and Stopping Multi-Parameter Bandit Processes....Pages 339-372
Bounded Variation Control of a Damped Linear Oscillator Under Random Disturbances....Pages 373-394
Existence of Densities for Statistics in the Cubic Sensor Problem....Pages 395-407
Piecewise Linear Filtering....Pages 409-428
Quick Simulation of Excessive Backlogs in Networks of Queues....Pages 429-437
On Some Perturbation Problems in Optimal Stopping and Impulse Control....Pages 439-472
Optimal Control of Jump-Markov Processes and Viscosity Solutions....Pages 473-500
An Introduction to Singular Stochastic Control....Pages 501-511
Scheduling, Routing, and Flow Control in Stochastic Networks....Pages 513-528
Product Expansions of Exponential Lie Series and the Discretization of Stochastic Differential Equations....Pages 529-561
A Survey of Large Time Asymptotics of Simulated Annealing Algorithms....Pages 563-582
Stochastic Scheduling on Parallel Processors and Minimization of Concave Functions of Completion Times....Pages 583-599
....Pages 601-609