Topics in Probability: Controlled Diffusion Processes, Math 8691, Fall 1997

Topics include

• Connections with fully nonlinear elliptic and parabolic equations, in particular, elliptic and parabolic Monge-Ampère equations
• General properties of value functions (like Bellman's principle)
• Existence and uniqueness of solutions of Bellman's equations
• -estimates of distribution densities of stochastic integrals
• Finding optimal and -optimal policies
• Viscosity solutions approach to stochastic control
• Numerical approximations of the solutions
• Controlled processes in domains

Some homework will be assigned and will form part of the final grade.

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