Mathematics – Probability
Scientific paper
2012-04-26
Mathematics
Probability
Submitted to: Electron. Commun. Probab
Scientific paper
The probability density function of the positive occupation time of one-dimensional Brownian motion with two-valued drift is derived by using the Feynman-Kac formula and Laplace transforms. The result is applied to a simple, two-dimensional stochastic differential equation describing stochastically perturbed sliding motion of a discontinuous, piecewise-smooth vector field. Long time asymptotics of the density are also computed.
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