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

2025/09/16 by Bobrowski, Adam, Pilipenko, Andrey
#47D07 #60J35 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2509.13076

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.

Citations

• The Parabolic Differential Equations and the Associated Semi-Groups of Transformations

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