Year: 2025
Type: article
Abstract: In this paper, we present a comprehensive study on the generalizations of skew Brownian motion and skew sticky Brownian motion by considering non-local operators at the origin for the heat equations on the real line. To begin, we introduce Marchaud-type operators and Caputo–Dzherbashian-type operators, providing an in-depth exposition of their fundamental properties. Subsequently, we describe the two stochastic processes and the associated equations. The non-local skew Brownian motion exhibits jumps, as a subordinator, at zero where the sign of the jump is determined by a skew coin. Conversely, the non-local skew sticky Brownian motion displays stickiness at zero, behaving as the inverse of a subordinator, resulting in non-Markovian dynamics.
Source: Journal of Evolution Equations
Author: Fausto Colantoni
Institution: Sapienza University of Rome
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
Award: G5245466801
OpenAlex ID: W4409158444