Mathematical Sciences: Non-adapted Stochastic Differential Systems

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The principal investigator will study non-adaptive differential systems. Non-adaptive differential systems are stochastic (random) differential equations whose solutions are not adapted to the driving noise, either because the coefficients of the equation anticipate the noise or because boundary conditions are imposed at the final time. The investigator will continue to study such systems by using a new stochastic calculus developed by Nualart and Pardoux for stochastic integral with anticipating integrands. One aspect of the research involves collaboration with E. Pardoux. They will investigate Markov field properties and filtering for stochastic bilinear equations with boundary conditions.