A Limit Theorem for Certain Feller Semigroups, and the Distribution of the Local Time for Brownian Motion When it Exits an Interval
Abstract
Within the framework of the theory of semigroups of operators, we consider a local singular perturbation of a one-dimensional Laplace operator. The Feller semigroups we study describe Brownian motions on an interval with killing that is more and more concentrated around a chosen point. As a result, the description of the limit semigroup involves a Robin-type boundary condition that reflects the killing mechanism that applies to this point and to this point only. As an application we provide a semigroup-theoretical approach to calculating the distribution of the local time for Brownian motion when it exits an interval.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Stochastic processes and financial applications
advanced mathematical theories
Publication details
- Journal / source
- Results in Mathematics
- Volume
- 81
- Issue
- 6
- Publication date
- 29 August 2026
- Language
- EN