2015/03/16 by Jorge Ramírez, Edward C. Waymire, Ramirez, Jorge M. +3
Economics, Econometrics and Finance · Physics and Astronomy · #60G17 #60G51 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1503.04660
openalex publication_date 2015/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.