| Abstract: |
| In this talk, we consider the Cauchy problem for backward stochastic partial differential equations (BSPDEs) involving fractional Laplacian operator. By employing the martingale representation theorem and the fractional heat kernel, we construct an explicit form of the solution, thereby demonstrating the existence and uniqueness of a strong solution in Holder space. Utilizing the freezing coefficients method as well as the continuation method, we establish Holder estimates for general BSPDEs with random coefficients dependent on space time variables. As an application, we use the fractional adjoint equation to study stochastic optimal control of the partially observed systems driven by Levy processes. This work is jointed with Yuyang Ye and Shanjian Tang. |
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