Continuity of Local Time: An Applied Perspective

Jorge M. Ramirez (), Enirque A. Thomann () and Edward C. Waymire ()
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Jorge M. Ramirez: Universidad Nacional de Colombia
Enirque A. Thomann: Oregon State University
Edward C. Waymire: Oregon State University

A chapter in The Fascination of Probability, Statistics and their Applications, 2016, pp 191-207 from Springer

Abstract: 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.

Keywords: Dispersion; Discontinuous diffusion; Skew brownian motion; Semi-martingale local time; Diffusion local time; Occupation time (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-25826-3_9

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DOI: 10.1007/978-3-319-25826-3_9

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