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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 finite size winding center.
The condition of thermal equilibrium simplifies the theoretical treatment of fluctuations as found in the celebrated Einsteins relation between mobility and diffusivity for Brownian motion. Several recent theories relax the hypothesis of thermal equi
Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic correlation tim
We study statistical properties of the process $Y(t)$ of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion $X(t)$ with the Hurst index $H in (0,1)$. We show th
Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $Hin [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical applications a
We study the stochastic motion of particles driven by long-range correlated fractional Gaussian noise in a superharmonic external potential of the form $U(x)propto x^{2n}$ ($ninmathbb{N}$). When the noise is considered to be external, the resulting o