Asymptotic relation for the density of a multidimensional random evolution with rare poisson switchings - Kolesnik, A. D. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
In the Euclidean space R^m,m ≥ 2, the symmetric random evolution X(t) = (X_1(t),...,X_m(t)) controlled by a homogeneous Poisson process with parameter λ > 0 is considered. An asymptotic formula for the transition density p(x,t),t > 0, of the process X(t) for λ → 0 is obtained. The behavior of p(x,t) near the boundary of the diffusion area in spaces of various dimensions is described.