Related papers: L\'evy Ratchet in a Weak Noise Limit: Theory and S…
We study the decoherence of a one-particle system, whose classical correpondent is chaotic, when it evolves coupled to a weak quenched environment. This is done by analytical evaluation of the Loschmidt Echo, (i.e. the revival of a…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
In this paper we analyze a L\'evy process reflected at a general (possibly random) barrier. For this process we prove Central Limit Theorem for the first passage time. We also give the finite-time first passage probability asymptotics.
The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either…
Numerical evidence of directed transport driven by symmetric Levy noise in time-independent ratchet potentials in the absence of an external tilting force is presented. The results are based on the numerical solution of the fractional…
In this paper, we first explore certain structural properties of L\'evy flows and use this information to obtain the existence of strong solutions to a class of Stochastic PDEs in the space of tempered distributions, driven by L\'evy noise.…
In this article we give sufficient and necessary conditions for the existence of a weak and mild solution to stochastic evolution equations with (general) L\'{e}vy noise taking values in the dual of a nuclear space. As part of our approach…
The Langevin equation for a particle (`random walker') moving in d-dimensional space under an attractive central force, and driven by a Gaussian white noise, is considered for the case of a power-law force, F(r) = - Ar^{-sigma}. The…
In the present paper, a new and simple approach is provided for proving rigorously that for general L\'evy financial markets the minimal entropy martingale measure and the Esscher martingale measure coincide. The method consists in…
We study a two-dimensional diffusive motion of a tracer particle in restricted, crowded anisotropic geometries. The underlying medium is the same as in our previous work [J. Chem. Phys. 140, 044706 (2014)] in which standard, gaussian…
We investigate the self-propulsion of an inertial active particle confined in a two-dimensional harmonic trap. The particle is suspended in a non-Newtonian or viscoelastic suspension with a friction kernel that decays exponentially with a…
Multiple scattering is a process in which a particle is repeatedly deflected by other particles. In an overwhelming majority of cases, the ensuing random walk can successfully be described through Gaussian, or normal, statistics. However,…
L\'{e}vy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a…
The underdamped Langevin equation of motion of a particle, in a symmetric periodic potential and subjected to a symmetric periodic forcing with mean zero over a period, with nonuniform friction, is solved numerically. The particle is shown…
We study a stochastic optimization problem in which the sampling distribution depends on the decision variable, and the available samples are generated through an iterate-dependent Markov chain. Such settings arise naturally in problems…
We derive explicit results for the asymptotic probability density and drift velocity in systems driven by dichotomous Markov noise, including the situation in which the asymptotic dynamics crosses {\em unstable} fixed points. The results…
We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat''…
We consider an inertial active Ornstein-Uhlenbeck particle self-propelling in a saw-tooth ratchet potential. Using the Langevin simulation and matrix continued fraction method, the particle transport, steady state diffusion, and coherence…
For a multivariate L\'evy process satisfying the Cram\'er moment condition and having a drift vector with at least one negative component, we derive the exact asymptotics of the probability of ever hitting the positive orthant that is being…
L\'evy processes, known for their ability to model complex dynamics with skewness, heavy tails and discontinuities, play a critical role in stochastic modeling across various domains. However, inference for most L\'evy processes, whether in…