On planar Brownian motion singularly tilted through a point potential
Location
Room 321, Hume Hall
Start Date
27-4-2024 10:00 AM
End Date
27-4-2024 11:00 AM
Description
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 Schrödinger operator with a point potential at the origin. Although, in a few ways, our processes of interest are closely related to twodimensional 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
conference proceeding
Recommended Citation
Clark, Jeremy and Mian, Barkat, "On planar Brownian motion singularly tilted through a point potential" (2024). AMS-AWM Student Research Symposium. 12.
https://egrove.olemiss.edu/ams_awm_sympo/2024/schedule/12
On planar Brownian motion singularly tilted through a point potential
Room 321, Hume Hall
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 Schrödinger operator with a point potential at the origin. Although, in a few ways, our processes of interest are closely related to twodimensional 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.
Comments
poster