Continuity of Local Time: An applied perspective
Abstract
Continuity of local time for Brownian motion ranks among the most notable mathematical results in the theory of stochastic processes. This article addresses its implications from the point of view of applications. In particular an extension of previous results on an explicit role of continuity of (natural) local time is obtained for applications to recent classes of problems in physics, biology and finance involving discontinuities in a dispersion coefficient. The main theorem and its corollary provide physical principles that relate macro scale continuity of deterministic quantities to micro scale continuity of the (stochastic) local time.
Cite
@article{arxiv.1503.04660,
title = {Continuity of Local Time: An applied perspective},
author = {Jorge M. Ramirez and Edward C. Waymire and Enrique A. Thomann},
journal= {arXiv preprint arXiv:1503.04660},
year = {2015}
}
Comments
To appear in: "The fascination of Probability, Statistics and Their Applications. In honour of Ole E. Barndorff-Nielsen on his 80th birthday"