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We study the connection between the parameters of the fractional Fokker-Planck equation, which is associated with the overdamped Langevin equation driven by noise with heavy-tailed increments, and the transition probability density of the noise generating process. Explicit expressions for these parameters are derived both for finite and infinite variance of the rescaled transition probability density.
We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a set of self-reproducing solutions. Explicit cases are reported and stud
In this paper we statistically analyze the Fokker-Planck (FP) equation of Schramm-Loewner evolution (SLE) and its variant SLE($kappa,rho_c$). After exploring the derivation and the properties of the Langevin equation of the tip of the SLE trace, we o
We investigate the diffusion of particles in an attractive one-dimensional potential that grows logarithmically for large $|x|$ using the Fokker-Planck equation. An eigenfunction expansion shows that the Boltzmann equilibrium density does not fully
We consider the $d=1$ nonlinear Fokker-Planck-like equation with fractional derivatives $frac{partial}{partial t}P(x,t)=D frac{partial^{gamma}}{partial x^{gamma}}[P(x,t) ]^{ u}$. Exact time-dependent solutions are found for $ u = frac{2-gamma}{1+ ga
We derive the generalized Fokker-Planck equation associated with the Langevin equation (in the Ito sense) for an overdamped particle in an external potential driven by multiplicative noise with an arbitrary distribution of the increments of the noise