In this talk we'll consider the filtering and prediction problem for a partially observed diffusion process. Usually measure-valued stochastic partial differential equations (SPDEs) are derived for the filtering and prediction measures. These equations can be hard to solve numerically. We provide an approximation algorithm using conditional generative adversarial networks (GANs) and signatures, an object from rough path theory. We use controlled differential equations (CDEs) as universal approximators to propose an estimator for the conditional and prediction law. We show well-posedness in providing a rigorous mathematical framework. Numerical results show the efficiency of our algorithm.
Fabian Germ is a PhD student at the University of Edinburgh, working with Istvan Gyongy on filtering for jump-diffusion processes and related SPDEs. Prior to that he obtained a Master's degree at the University of Waterloo, Canada, as well as undergraduate degrees in Mathematics and Physics from the TU Vienna.
While finishing his PhD, he became interested in signature methods through a side project with a colleague. He is looking forward to working more on the use of signatures and rough paths in estimation theory.
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