Stochastic processes associated to multidimensional parabolic transmission problems in divergence form

Pierre Etoré (1) , Miguel Martinez (2)

1 IPS - Inférence Processus Stochastiques
2 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

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.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Pierre Etoré, Miguel Martinez. Stochastic processes associated to multidimensional parabolic transmission problems in divergence form. 2022. ⟨hal-02531467v2⟩