On constructing a sticky membrane located on a given surface for a symmetric α-stable process

M. M. Osypchuk, M. I. Portenko
Theory of Stochastic Processes
Vol.23 (39), no.1, 2018, pp.66-72
For a symmetric α-stable stochastic process with α∈ (1,2) in a Euclidean space, a membrane located on a fixed bounded closed surface S is constructed in such a way that the points of the surface possess the property of delaying the process with some given positive coefficient (p(x))_{x ∈ S}. In other words, the points of S are sticky for the process constructed. We show that this process is associated with some initial-boundary value problem for pseudo-differential equations related to a symmetric α-stable process.