Path integral approach to Brownian motion driven with an ac force.

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

Diffusion in periodic potentials with path integral hyperdynamics.

We consider the diffusion of brownian particles in one-dimensional periodic potentials as a test bench for the recently proposed stochastic path integral hyperdynamics (PIHD) scheme [Chen and Horing, J. Chem. Phys. 126, 224103 (2007)]. First, we consider the case where PIHD is used to enhance the transition rate of activated rare events. To this end, we study the diffusion of a single brownian ...

Stochastic differential equations driven by fractional Brownian motions

2 Young’s integrals and stochastic differential equations driven by fractional Brownian motions 4 2.1 Young’s integral and basic estimates . . . . . . . . . . . . . . . . . . 4 2.2 Stochastic differential equations driven by a Hölder path . . . . . . . 7 2.3 Multidimensional extension . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Fractional calculus . . . . . . . . . . . . . . . . . . . ...

Injected Power Fluctuations in Langevin Equation

Using path integral method, we compute exactly the probability density function of the power (averaged over a large time interval of length τ) injected (and dissipated) by the random force into a Brownian particle driven by a Langevin equation. The resulting distribution, as well as the associated large deviation function, display strong asymmetry, whose origin is discussed. Moreover, the so-ca...

Fractional Lévy motion through path integrals

Abstract. Fractional Lévy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The f...