Stochastic processes associated to multidimensional parabolic transmission problems in divergence form
Pierre Étoré, Miguel Martínez · Latin American Journal of Probability and Mathematical Statistics · 2023
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 Fukushima et al. (1994) and Stroock (1988) 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.