The Positive Occupation Time of Brownian Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise

David J. W. Simpson; Rachel Kuske

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arXiv · 1204.5985

The Positive Occupation Time of Brownian Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise

David J. W. Simpson·Rachel Kuske

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Abstract

We derive the probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift. Long time asymptotics of the density are also computed. We use the result to describe the transitional probability density function of a general N-dimensional system of stochastic differential equations representing stochastically perturbed sliding motion of a discontinuous, piecewise-smooth vector field on short time frames. A description of the density at larger times is obtained via an asymptotic expansion of the Fokker-Planck equation.

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BibTeX RIS

David J. W. Simpson, Rachel Kuske. 2012-04-26. The Positive Occupation Time of Brownian Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise. https://arxiv.org/abs/1204.5985

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