Abstract
A symmetric random evolution X(t) = (X 1 (t), …, X m (t)) controlled by a homogeneous Poisson process with parameter λ > 0 is considered in the Euclidean space ℝ m , m ≥ 2. We obtain an asymptotic relation for the transition density p(x, t), t > 0, of the process X(t) as λ → 0 and describe the behavior of p(x, t) near the boundary of the diffusion domain in spaces of different dimensions.
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