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On the double Laplace transform of the truncated variation of a Brownian motion with drift

Part of: Distribution theory - Probability Stochastic processes

Published online by Cambridge University Press:  01 October 2016

Rafał Marcin Łochowski
Rafał Marcin Łochowski*
Affiliation:
Department of Mathematics and Mathematical Economics, ul. Madalińskiego 6/8, 02-513 Warsaw, Poland email rlocho314@gmail.com African Institute for Mathematical Sciences, 5 Melrose Road, Muizenberg, Cape Town 7945, South Africa

Abstract

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The aim of this paper is to find a formula for the double Laplace transform of the truncated variation of a Brownian motion with drift. In order to find the double Laplace transform, we also prove some identities for the Brownian motion with drift, which may be of independent interest.

MSC classification

Primary: 60E10: Characteristic functions; other transforms
Secondary: 60G15: Gaussian processes
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 281 - 292
Copyright
© The Author 2016 

References

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