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On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions
2022-11-09 · via math.PR updates on arXiv.org

The Bessel process in low dimension (0 $\le$ $δ$ $\le$ 1) is not an It{ô} process and it is a semimartingale only in the cases $δ$ = 1 and $δ$ = 0. In this paper we first characterize it as the unique solution of an SDE with distributional drift or more precisely its related martingale problem. In a second part, we introduce a suitable notion of path-dependent Bessel processes and we characterize them as solutions of path-dependent SDEs with distributional drift.

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