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

2022/11/09 by Ohashi, Alberto, Russo, Francesco, Teixeira, Alan
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2211.04859

Abstract

The Bessel process in low dimension (0 ≤ δ ≤ 1) is not an Itô 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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