Conditional Law and Occupation Times of Two-Sided Sticky Brownian Motion

Bugra Can; Mine Caglar

doi:10.1016/j.spl.2020.108856

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arXiv · 1910.10213

Conditional Law and Occupation Times of Two-Sided Sticky Brownian Motion

Bugra Can·Mine Caglar

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Abstract

Sticky Brownian motion on the real line can be obtained as a weak solution of a system of stochastic differential equations. We find the conditional distribution of the process given the driving Brownian motion, both at an independent exponential time and at a fixed time t>0. As a classical problem, we find the distribution of the occupation times of a half-line, and at 0, which is the sticky point for the process.

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Bugra Can, Mine Caglar. 2019-10-22. Conditional Law and Occupation Times of Two-Sided Sticky Brownian Motion. https://doi.org/10.1016/j.spl.2020.108856

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