ON SDEs FOR BESSEL PROCESSES IN LOW DIMENSION AND PATH-DEPENDENT EXTENSIONS - Archive ouverte HAL Access content directly
Journal Articles ALEA : Latin American Journal of Probability and Mathematical Statistics Year : 2023

ON SDEs FOR BESSEL PROCESSES IN LOW DIMENSION AND PATH-DEPENDENT EXTENSIONS

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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Dates and versions

hal-03844769 , version 1 (09-11-2022)
hal-03844769 , version 2 (11-08-2023)

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Alberto Ohashi, Francesco Russo, Alan Teixeira. ON SDEs FOR BESSEL PROCESSES IN LOW DIMENSION AND PATH-DEPENDENT EXTENSIONS. ALEA : Latin American Journal of Probability and Mathematical Statistics, In press. ⟨hal-03844769v2⟩
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