Approximations to and Local Properties of Diffusion with Discontinuous Controls,
BROWN UNIV PROVIDENCE R I DIV OF APPLIED MATHEMATICS
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The stochastic differential Ito equation 1, dx fx,t,ux,tdt sigmax,tdz, where z sub t is a Wiener process, is a common model of a variety of stochastic control systems. Recently, in a paper by Rishel, a transformation of Girsanov was applied to construct a process of the form 1 where u is allowed to be merely bounded and measurable, and proved some theorems concerning the relationship between the formal dynamic programming equation for the cost, and the optimal control. Several questions remain open for the constructed papers by Rishel and Girsanov. As u is not necessarily uniformly Lipschitz, the question of uniqueness remains, and is discussed in this report.
- Statistics and Probability