Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties

Elena Bandini; Francesco Russo

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arXiv · 2211.03444

Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties

Elena Bandini·Francesco Russo

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Abstract

We discuss a concept of path-dependent SDE with distributional drift with possible jumps. We interpret it via a suitable martingale problem, for which we provide existence and uniqueness. The corresponding solutions are expected to be Dirichlet processes, nevertheless we give examples of solutions which do not fulfill this property. In the second part of the paper we indeed state and prove significant new results on the class of Dirichlet processes.

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Elena Bandini, Francesco Russo. 2022-11-07. Path-dependent SDEs with jumps and irregular drift: well-posedness and Dirichlet properties. https://arxiv.org/abs/2211.03444

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