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

Alberto Ohashi; Francesco Russo; Alan Teixeira

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

Probability 2022-11-10 v1

Authors: Alberto Ohashi , Francesco Russo , Alan Teixeira

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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@article{arxiv.2211.04859,
  title  = {On Sdes For Bessel Processes In Low Dimension And Path-dependent Extensions},
  author = {Alberto Ohashi and Francesco Russo and Alan Teixeira},
  journal= {arXiv preprint arXiv:2211.04859},
  year   = {2022}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2002.02384

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

Abstract

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