On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions

Alberto Ohashi; Francesco Russo; Alan Teixeira

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arXiv · 2211.04859

On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions

Alberto Ohashi·Francesco Russo·Alan Teixeira

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Abstract

The Bessel process in low dimension (0 $\le$ $\delta$ $\le$ 1) is not an It{\^o} 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.

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Alberto Ohashi, Francesco Russo, Alan Teixeira. 2022-11-09. On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions. https://arxiv.org/abs/2211.04859

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