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A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval (2509.13076v1)
Published 16 Sep 2025 in math.PR
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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