On large deviation properties of Brownian motion with dry friction
arXiv:1407.5448 · doi:10.1103/PhysRevE.90.042102
Abstract
We investigate piecewise-linear stochastic models as with regards to the probability distribution of functionals of the stochastic processes, a question which occurs frequently in large deviation theory. The functionals that we are looking into in detail are related to the time a stochastic process spends at a phase space point or in a phase space region, as well as to the motion with inertia. For a Langevin equation with discontinuous drift, we extend the so-called backward Fokker-Planck technique for nonnegative support functionals to arbitrary support functionals, to derive explicit expressions for the moments of the functional. Explicit solutions for the moments and for the distribution of the so-called local time, the occupation time and the displacement are derived for the Brownian motion with dry friction, including quantitative measures to characterize deviation from Gaussian behaviour in the asymptotic long time limit.
arXiv comment16 pages, 11 figures
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- Velocity and displacement statistics in a stochastic model of nonlinear friction showing bounded particle speed
- Single Particle Brownian Motion with Solid Friction
- Exact probability distribution functions for Parrondo's games
- Numerical solutions of Fokker-Planck equations with drift-admitting jumps
- On energy dissipation in a friction-controlled slide of a body excited by random motions of the foundation