On two-dimensional Brownian motion singularly tilted through a point potential
Document Type
Lecture
Publication Date
4-6-2023
Abstract
A well-known but interesting characteristic of two-dimensional Brownian motion is that it will (almost surely) never return exactly to the origin even though it will reenter any given small neighborhood of the origin infinitely many times. I will discuss a two-dimensional diffusion process closely connected to Brownian motion that has just enough drift towards the origin to enable it to return there. This opens up the possibility of formulating a theory of its local time, a characterization of the time spent in the vicinity of the origin. The transition probabilities for this diffusion process are defined through an integration kernel that has arisen in recent articles on the two-dimensional stochastic heat equation. The work that I will present is in collaboration with Barkat Mian.
Relational Format
presentation
Recommended Citation
Clark, Jeremy, "On two-dimensional Brownian motion singularly tilted through a point potential" (2023). Probability & Statistics Seminar. 18.
https://egrove.olemiss.edu/math_statistics/18
