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.

Optimality of "full bang to reduce predicted miss" for some partially observed stochastic control problems.- On some approximation techniques in non-linear filtering.- Applications of Homogenization Theory to the control of flexible structures.- Control of Markov chains with long-run average cost criterion.- Automatic study in stochastic control.- Some results on Kolmogoroff equations for infinite dimensional stochastic systems.- Hamilton-Jacobi equations with constraints.- An approximate minimum principle for a partially observed Markov chain.- Generalized solutions in the optimal control of diffusions.- Consistency of maximum likelihood and pseudo-likelihood estimators for Gibbs Distributions.- Brownian models of queueing networks with heterogeneous customer populations.- Non-linear filtering - the degenerate case.- The asymptotic behaviour of the maximum likelihood estimates for a class of diffusion processes.- The filtering problem for infinite dimensional stochastic processes.- Stochastic control under finite-fuel constraints.- Recent advances in the theory of stochastic adaptive control.- Almost optimal controls for wideband noise driven systems.- Asymptotic solutions of bandit problems.- Viscosity solutions of second-order equations, stochastic control and stochastic differential games.- On the memory length of the optimal nonlinear filter.- Implementation issues for Markov decision processes.- Navigating and stopping multi-parameter bandit processes.- Bounded variation control of a damped linear oscillator under random disturbances.- The support of the law of a filter in C? topology.- Existence of densities for statistics in the cubic sensor problem.- Piecewise linear filtering.- Quick simulation of excessive backlogs in networks of queues.- On someperturbation problems in optimal stopping and impulse control.- Optimal control of jump-markov processes and viscosity solutions.- An introduction to singular stochastic control.- Scheduling, routing, and flow control in stochastic networks.- Product expansions of exponential Lie Series and the discretization of stochastic differential equations.- A survey of large time asymptotics of simulated annealing algorithms.- Stochastic scheduling on parallel processors and minimization of concave functions of completion times.