On SDEs for Bessel Processes in low dimension and path-dependent extensions (original) (raw)

On some path-dependent sdes involving distributional drifts

arXiv: Probability, 2020

This paper investigates some one-dimensional path-dependent SDEs, which includes an irregular (distributional) drift b′ depending on the present position. We treat essentially two cases: the first one concerns the case when the drift b′ is the derivative of a continuous function, the second one when b ′ is the derivative of a logarithmic or an Heaviside function. In the second framework, we characterize Bessel processes in low dimension as unique solutions to some suitable strong martingale problems and we consider then path-dependent extensions.

On path-dependent SDEs involving distributional drifts

Modern Stochastics: Theory and Applications, 2022

The paper presents the study on the existence and uniqueness (strong and in law) of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributions of a continuous function.