Work

Stochastic processes associated to multidimensional parabolic transmission problems in divergence form

Year: 2020

Type: preprint

Abstract: In this note we define and study the stochastic process $X$ in link with a parabolic transmission operator $(A,D(A))$ in divergence form. The transmission operator involves a diffraction condition along a transmission boundary. To that aim we gather and clarify some results coming from the theory of Dirichlet forms as exposed in [6] and [14] for general divergence form operators. We show that $X$ is a semimartingale and that it is solution of a stochastic differential equation involving partial reflections in the co-normal directions along the transmission boundary.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2004.02440

Authors: Etore, Pierre, Martinez, Miguel

Institutions: Laboratoire d’Analyse et de Mathématiques Appliquées, Le LAMA

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Labex Bézout

OpenAlex ID: W4287817751

Cites:

Cited by: 1

Related to: 10