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The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. In this paper, we derive a Fractional Fokker--Planck equation for the probability distribution of…
In this study, we investigate a porous medium-type flux limited reaction--diffusion equation that arises in morphogenesis modeling. This nonlinear partial differential equation is an extension of the generalized…
We theoretically show that the dynamics of a driven quantum harmonic oscillator subject to non-dissipative noise is formally equivalent to the single-particle dynamics propagating through an experimentally feasible dynamically-disordered…
We consider spatially extended conductance based neuronal models with noise described by a stochastic reaction diffusion equation with additive noise coupled to a control variable with multiplicative noise but no diffusion. We only assume a…
In this work we study the transport properties of non-interacting overdamped particles, moving on tilted disordered potentials, subjected to Gaussian white noise. We give exact formulas for the drift and diffusion coefficients for the case…
We discuss the dynamics of a Brownian particle under the influence of a spatially periodic noise strength in one dimension using analytical theory and computer simulations. In the absence of a deterministic force, the Langevin equation can…
This article considers the variational wave equation with viscosity and transport noise as a system of three coupled nonlinear stochastic partial differential equations. We prove pathwise global existence, uniqueness, and temporal…
The aim of this paper is to prove stability of traveling waves for integro-differential equations connected with branching Markov processes. In other words, the limiting law of the left-most particle of a (time-continuous) branching Markov…
We study the asymptotic behaviour, in the small noise limit, of stochastic travelling wave solutions to reaction-diffusion equations perturbed by Wright-Fisher noise. Such equations are predicted to display three distinct responses to noise…
The Langevin equation is ubiquitously employed to numerically simulate plasmas, colloids and electrolytes. However, the usual assumption of white noise becomes untenable when the system is subject to an external AC electric field. This is…
In this paper we establish the meta-stability of travelling waves for a class of reaction-diffusion equations forced by a multiplicative noise term. In particular, we show that the phase-tracking technique developed in…
We have derived exact Langevin equations for a model of quasispecies dynamics. The inherent multiplicative reaction noise is complex and its statistical properties are specified completely. The numerical simulation of the complex Langevin…
An extension and generalization of a recently presented approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For a stochastic process in N dimensions which is superimposed…
The generalised Langevin equation with a retarded friction and a double-well potential is solved. The random force is modelled by a multiplicative noise with long jumps. Probability density distributions converge with time to a distribution…
We consider a process given as the solution of a stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. Explicit and optimal bounds for the Lebesgue density of that…
We study the non-equilibrium dynamics of solitons in model Hamiltonians for Peierls dimerized quasi-one dimensional conducting polymers and commensurate charge density wave systems. The real time equation of motion for the collective…
The nonlinear boson diffusion equation is taken as a basis to account for the fast thermalization of gluons in the initial stages of relativistic heavy-ion collisions. For constant drift and diffusion coefficients with schematic initial…
We study the impact of Brownian noise on transitions between metastable equilibrium states in a stochastic ice sheet model. Two methods to accomplish different objectives are employed. The maximal likely trajectory by maximizing the…
Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results have indicated transport by…
We present a theoretical approach to solve Markovian master equation for quantum transport with stochastic telegraph noise. Considering probabilities as functionals of a random telegraph process we use the Novikov's functional method to…