Han Cheng Lie (University of Potsdam)
The estimation of statistics of functionals of a diffusion process is a problem that arises in multiple applications. An example of such a problem involves estimating the expected value of the first exit time of a diffusion process from a bounded domain. One approach to estimating such statistics involves importance sampling via a change of measure, where the optimal change of measure is unique and yields a zero-variance estimator. Finding the optimal change of measure can be formulated as a stochastic optimal control problem, which can be solved computationally using gradient descent-based methods. We analyse a class of stochastic optimal control problems with the aim of understanding the convergence of gradient descent-based methods.
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