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

Alberto Ohashi (1) , Francesco Russo (2, 3) , Alan Teixeira (2, 3)

1 UnB - Universidade de Brasilia [Brasília]
2 ENSTA Paris - École Nationale Supérieure de Techniques Avancées
3 OC - Optimisation et commande

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.

Mots clés: SDEs with distributional drift; Bessel processes; pPath-dependent stochastic differential equations.

Domaines: Probabilités [math.PR]

Alberto Ohashi, Francesco Russo, Alan Teixeira. ON SDEs FOR BESSEL PROCESSES IN LOW DIMENSION AND PATH-DEPENDENT EXTENSIONS. 2022. ⟨hal-03844769v1⟩