%0 Generic %1 simpson2012positive %A Simpson, David J. W. %A Kuske, Rachel %D 2012 %K Brownian_motion diffusions local_time %T The Positive Occupation Time of Brownian Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise %U http://arxiv.org/abs/1204.5985 %X 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.

@misc{simpson2012positive, 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.}, added-at = {2015-10-07T05:28:02.000+0200}, author = {Simpson, David J. W. and Kuske, Rachel}, biburl = {https://www.bibsonomy.org/bibtex/23b721de092cacc08ca58efe059c884ed/peter.ralph}, description = {Basic result from Karatzas and Shreve, "Trivariate Density of Brownian Motion, Its Local and Occupation Times, with Application to Stochastic Control"}, interhash = {6cc3ba8a15d07c9a1f383ced920bdb3e}, intrahash = {3b721de092cacc08ca58efe059c884ed}, keywords = {Brownian_motion diffusions local_time}, note = {cite arxiv:1204.5985}, timestamp = {2015-10-07T05:28:02.000+0200}, title = {The Positive Occupation Time of {Brownian} Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise}, url = {http://arxiv.org/abs/1204.5985}, year = 2012 }