On planar Brownian motion singularly tilted through a point potential
Document Type
Lecture
Publication Date
4-25-2024
Abstract
We will discuss a special family of two-dimensional diffusions, defined over a finite time interval [0, T]. These diffusions have transition density functions that are given by the integral kernels of the semigroup corresponding to the two-dimensional Schrodinger operator with a point potential at the origin. Although, in a few ways, our processes of interest are closely related to two-dimensional Brownian motion, they have a singular drift pointing in the direction of the origin that is strong enough to enable the possibly of visiting there with positive probability. Our main focus is on characterizing a local time process at the origin for these diffusions analogous to that for a one-dimensional Brownian motion.
Relational Format
presentation
Recommended Citation
Mian, Barkat, "On planar Brownian motion singularly tilted through a point potential" (2024). Probability & Statistics Seminar. 6.
https://egrove.olemiss.edu/math_statistics/6
