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Asymptotic relation for the density of a multidimensional random evolution with rare poisson switchings

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Ukrainian Mathematical Journal Aims and scope

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 ℝm, 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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1631 – 1641, December, 2008.

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Kolesnik, A.D. Asymptotic relation for the density of a multidimensional random evolution with rare poisson switchings. Ukr Math J 60, 1915–1926 (2008). https://doi.org/10.1007/s11253-009-0180-6

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  • DOI: https://doi.org/10.1007/s11253-009-0180-6

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