Manuela L. BUJORIANU	Analytic methods in Control Engineering ACE

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Most common analytical methods for stochastic processes such as - stochastic dynamic programming, - variational methods, - martingale methods, - Dynkin's formula, - Girsanov's theorem, - large deviations - balayage and reduced function methods, - operator semigroup, - optimal stopping results, - Stochastic Lyapunov functions that are applied in the context of stochastic hybrid processes.

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Stochastic control is the study of dynamical systems subject to random perturbations and which can be controlled in order to optimize some performance criterion. Historically handled with Bellman's and Pontryagin's optimality principles, the research on control theory considerably developed over these last years, inspired in particular by problems emerging from mathematical finance. The global approach for studying stochastic control problems by the Bellman dynamic programming principle has now its suitable framework with viscosity solutions concept: this allows going beyond the classical verification Bellman approach for studying degenerate singular control.

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Applied stochastic control of jump diffusions

Bernt Karsten Øksendal, Agnès Sulem - 2005 - 208 pages The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.

Numerical methods for stochastic control problems in continuous time

Harold Joseph Kushner, Paul Dupuis - 2001 - 475 pages It covers effective numerical methods for stochastic control problems in continuous time on two levels, that of practice and that of mathematical development. It is broadly accessible for graduate students and researchers.

Stochastic control by functional analysis methods

Alain Bensoussan - 1982 - 410 pages

Controlled Markov processes and viscosity solutions

Wendell Helms Fleming, H. Mete Soner - 2006 - 428 pages This book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions.