Related papers: Fractional transport equations for Levy stable pro…
This paper is devoted to the fractional generalization of the Fokker-Planck equation associated with a stochastic differential equation in a bounded domain. The driving process of the stochastic differential equation is a L\'evy process…
Transport of the Brownian particles driven by L\'evy flights coexisting with subdiffusion in asymmetric periodic potentials is investigated in the absence of any external driving forces. Using the Langevin-type dynamics with subordination…
A quantum Smoluchowski equation is put forward that consistently describes thermal quantum states. In particular, it notably does not induce a violation of the second law of thermodynamics. This so modified kinetic equation is applied to…
Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…
The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in…
In this paper we study Doob's transform of fractional Brownian motion (FBM). It is well known that Doob's transform of standard Brownian motion is identical in law with the Ornstein-Uhlenbeck diffusion defined as the solution of the…
We consider stochastic differential equations (SDEs) driven by a fractional Brownian motion with a drift coefficient that is allowed to be arbitrarily close to criticality in a scaling sense. We develop a comprehensive solution theory that…
We study the behavior of skyrmions in thin films under the action of stochastic torques arising from thermal fluctuations. We find that the Brownian motion of skyrmions is described by a stochastic Thiele's equation and its corresponding…
In this paper, we consider the nonparametric estimation problem of the drift function of stochastic differential equations driven by $\alpha$-stable L\'{e}vy motion. First, the Kullback-Leibler divergence between the path probabilities of…
The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is…
We derive some fluid-dynamic models for electron transport near a Dirac point in graphene. We start from a kinetic model constituted by a set of spinorial Wigner equations, we make suitable scalings (hydrodynamic or diffusive) of the model…
We consider fractional directional derivatives and establish some connection with stable densities. Solutions to advection equations involving fractional directional derivatives are presented and some properties investigated. In particular…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by…
Transport events in turbulent tokamak plasmas often exhibit non-local or non-diffusive action at a distance features that so far have eluded a conclusive theoretical description. In this paper a theory of non-local transport is investigated…
Inspired on the continued-fraction technique to solve the classical Fokker--Planck equation, we develop continued-fraction methods to solve quantum master equations in phase space (Wigner representation of the density matrix). The approach…
Fractional tempered stable motion (fTSm)} is defined and studied. FTSm has the same covariance structure as fractional Brownian motion, while having tails heavier than Gaussian but lighter than stable. Moreover, in short time it is close to…
Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using…
Recent experiments of fluid transport in nano-channels have shown evidence of a coupling between charge-fluctuations in polar fluids and electronic excitations in graphene solids, which may lead to a significant reduction of friction a…
Consider the bidomain equations from electrophysiology with FitzHugh--Nagumo transport subject to current noise, i.e., subject to stochastic forcing modeled by a cylindrical Wiener process. It is shown that this set of equations admits a…
Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum…