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On the Distribution Density of the First Exit Point of a Diffusion Process with Break from a Small Circular Neighborhood of Its Initial Point

A two-dimensional homogeneous diffusion process with break is considered. The distribution of the first exit point of such a process from an arbitrary neighborhood of zero as a function of the initial point of the process is determined by an elliptic second order partial differential equation with constant coefficients and corresponds to the solution of the Dirichlet problem for this equation. A connection of this Dirichlet problem with the distribution density of the first exit point of the process from a small circular neighborhood of zero is established. In terms of this asymptotic, we find necessary and sufficient conditions under which a function of the initial point of the process satisfies a particular second order elliptical partial differential equation that corresponds to a standard Wiener process with drift and break.

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Correspondence to B. P. Harlamov.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 486, 2019, pp. 286–302.

Translated by S. Yu. Pilyugin.

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Harlamov, B.P. On the Distribution Density of the First Exit Point of a Diffusion Process with Break from a Small Circular Neighborhood of Its Initial Point. J Math Sci 258, 935–946 (2021). https://doi.org/10.1007/s10958-021-05593-y

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