On oscillating sticky Brownian motion
Probability
2023-02-08 v1
Abstract
Starting with a Brownian motion, we define and study a novel diffusion process by combining stickiness and oscillation properties. The associated stochastic differential equation, resolvent and semigroup are provided. Also the trivariate density of position, local time and occupation time of this diffusion is obtained explicitly. Furthermore, we give a construction of two Brownian motions with drift and scaling whose difference is an oscillating sticky Brownian motion, up to a multiplicative constant.
Cite
@article{arxiv.2302.03125,
title = {On oscillating sticky Brownian motion},
author = {Wajdi Touhami},
journal= {arXiv preprint arXiv:2302.03125},
year = {2023}
}