A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval

Adam Bobrowski; Andrey Pilipenko

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arXiv · 2509.13076

A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval

Adam Bobrowski·Andrey Pilipenko

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Abstract

We consider local singular perturbations of a one-dimensional Laplace operator from the point of view of semigroup theory. Under certain assumptions, we prove the convergence of the corresponding semigroups to the heat semigroup with Robin-type boundary conditions at zero. As an application we provide semigroup theoretical approach to calculating the distribution of the local time for Brownian motion when it exits an interval.

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Adam Bobrowski, Andrey Pilipenko. 2025-09-16. A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval. https://arxiv.org/abs/2509.13076

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