Fractional Brownian motion in presence of two fixed adsorbing boundaries
نویسنده
چکیده
Abstract. We study the long-time asymptotics of the probability Pt that the Riemann-Liouville fractional Brownian motion with Hurst index H does not escape from a fixed interval [−L, L] up to time t. We show that for any H ∈]0, 1], for both subdiffusion and superdiffusion regimes, this probability obeys ln(Pt) ∼ −t2H/L2, i.e. may decay slower than exponential (subdiffusion) or faster than exponential (superdiffusion). This implies that survival probability St of particles undergoing fractional Brownian motion in a one-dimensional system with randomly placed traps follows ln(St) ∼ −n2/3t2H/3 as t → ∞, where n is the mean density of traps.
منابع مشابه
Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion
متن کامل
On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays
In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory
متن کاملEffects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium
This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...
متن کاملWinding Number of Fractional Brownian Motion
We find the exact winding number distribution of Riemann-Liouville fractional Brownian motion for large times in two dimensions using the propagator of a free particle. The distribution is similar to the Brownian motion case and it is of Cauchy type. In addition we find the winding number distribution of fractal time process, i.e., time fractional Fokker-Planck equation, in the presence of fini...
متن کاملDetecting origins of subdiffusion: P-variation test for confined systems.
In this paper, we propose a method to distinguish between mechanisms leading to single molecule subdiffusion in confinement. We show that the method of p-variation, introduced in the recent paper [M. Magdziarz, Phys. Rev. Lett. 103, 180602 (2009)], can be successfully applied also for confined systems. We propose a test which allows distinguishing between heavy-tailed continuous-time random wal...
متن کامل