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

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Bobrowski, Adam, Pilipenko, Andrey
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866918142203133952
author Bobrowski, Adam
Pilipenko, Andrey
author_facet Bobrowski, Adam
Pilipenko, Andrey
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_13076
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval
Bobrowski, Adam
Pilipenko, Andrey
Probability
60J35, 47D07
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.
title A limit theorem for certain Feller semigroups, and the distribution of the local time for Brownian motion when it exits an interval
topic Probability
60J35, 47D07
url https://arxiv.org/abs/2509.13076