Controlled Diffusion Processes

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This book deals with the optimal control of solutions of fully observable Itô-type stochastic differential equations. The validity of the Bellman differential equation for payoff functions is proved and rules for optimal control strategies are developed. Topics include optimal stopping, one dimensional controlled diffusion, the Lp-estimates of stochastic integral distributions, the existence theorem for stochastic equations, the Itô formula for functions, and the Bellman principle, equation, and normalized equation.