Skew Brownian motion with dry friction: Joint density approach

This note concerns the distribution of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in Berezin and Zayats (2019) by using the Laplace transform and joint characteristic functions. We provide an alternative approach, which is based on the use of th...

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Bibliographic Details
Published inStatistics & probability letters Vol. 187; p. 109511
Main Authors Gairat, Alexander, Shcherbakov, Vadim
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2022
Subjects
Caughey–Dienes process
Local time
Occupation time
Skew Brownian motion
Caughey–Dienes process
Occupation time
Local time
Skew Brownian motion
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Summary:This note concerns the distribution of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in Berezin and Zayats (2019) by using the Laplace transform and joint characteristic functions. We provide an alternative approach, which is based on the use of the joint density for Skew Brownian motion, its last visit to the origin, its local and occupation times derived in Gairat and Shcherbakov (2017).
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2022.109511