On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions
Abstract
The Bessel process in low dimension (0 $\le$ $\delta$ $\le$ 1) is not an It{ô} process and it is a semimartingale only in the cases $\delta$ = 1 and $\delta$ = 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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2022
- DOI:
- 10.48550/arXiv.2211.04859
- arXiv:
- arXiv:2211.04859
- Bibcode:
- 2022arXiv221104859O
- Keywords:
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- Mathematics - Probability
- E-Print:
- arXiv admin note: substantial text overlap with arXiv:2002.02384