On SDEs for Bessel Processes in low dimension and path-dependent extensions
2023
Publication type:
Paper in peer-reviewed journals
Journal:
ALEA, Lat. Am. J. Probab. Math. Sta., vol. 20, pp. 1111-1138
DOI:
HAL:
arXiv:
Keywords :
SDEs with distributional drift;
Bessel processes; path-dependent stochastic differential equations.
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
{\it path-dependent Bessel processes} and we characterize
them as solutions of path-dependent SDEs with distributional
drift.
BibTeX:
@article{Oha-Rus-Tei-2023,
author={Alberto Ohashi and Francesco Russo and Alan Teixeira },
title={On SDEs for Bessel Processes in low dimension and
path-dependent extensions },
doi={10.30757/ALEA.v20-41 },
journal={ALEA, Lat. Am. J. Probab. Math. Sta. },
year={2023 },
volume={20 },
pages={1111--1138},
}