Continuity of local time: An applied perspective

Jorge M. Ramirez; Enirque A. Thomann; Edward C. Waymire

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

Continuity of local time: An applied perspective

Jorge M. Ramirez
, Enirque A. Thomann
, Edward C. Waymire

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

1 Scopus citations

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.

Original language	English
Title of host publication	The Fascination of Probability, Statistics and their Applications
Subtitle of host publication	In Honour of Ole E. Barndorff-Nielsen
Publisher	Springer International Publishing
Pages	191-207
Number of pages	17
ISBN (Electronic)	9783319258263
ISBN (Print)	9783319258249
DOIs	https://doi.org/10.1007/978-3-319-25826-3_9
State	Published - Jan 1 2015
Externally published	Yes

Keywords

Diffusion local time
Discontinuous diffusion
Dispersion
Occupation time
Semimartingale local time
Skew brownian motion

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

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AU - Thomann, Enirque A.

AU - Waymire, Edward C.

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PY - 2015/1/1

Y1 - 2015/1/1

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AB - 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.

KW - Diffusion local time

KW - Discontinuous diffusion

KW - Dispersion

KW - Occupation time

KW - Semimartingale local time

KW - Skew brownian motion

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SP - 191

EP - 207

BT - The Fascination of Probability, Statistics and their Applications

PB - Springer International Publishing

ER -

Continuity of local time: An applied perspective

Abstract

Keywords

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