Skew Brownian motion with dry friction: joint density approach
Alexander Gairat, Vadim Shcherbakov
TL;DR
This paper presents an alternative method for deriving the distributions of Skew Brownian motion with dry friction and occupation time, utilizing existing results rather than Laplace transforms or joint characteristic functions.
Contribution
It introduces a new approach based on previous results for Skew Brownian motion, offering an alternative to traditional distribution derivations.
Findings
Derived distributions using the new approach
Validated the method against existing results
Simplified the derivation process
Abstract
This note concerns distributions of Skew Brownian motion with dry friction and its occupation time. These distributions were obtained in [2] by using the Laplace transform and joint characteristic functions. We provide an alternative approach to deriving these distributions. Our approach is based on using the results for Skew Brownian motion obtained in [3].
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Taxonomy
TopicsStochastic processes and financial applications · Complex Systems and Time Series Analysis · Stochastic processes and statistical mechanics