Related papers: An old efficient approach to anomalous Brownian mo…
Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to…
In this paper, the first microscopic approach to the Brownian motion is developed in the case where the mass density of the suspending bath is of the same order of magnitude as that of the Brownian (B) particle. Starting from an extended…
The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the traping phase) in a disordered medium is considered in the presence of an external…
In this work, we analyze the relaxation of a classical spin interacting with a heat bath, starting from the fully dynamical Hamiltonian description. An analogous problem in the framework of generalized Langevin equation (GLE) with anomalous…
We study a particular generalisation of the classical Kramers model describing Brownian particles in the external potential. The generalised model includes the stochastic force which is modelled as an additive random noise that depends upon…
Brownian oscillator, i.e. a micron-sized or smaller particle trapped in a thermally fluctuating environment is studied. The confining harmonic potential can move with a constant velocity. As distinct from the standard Langevin theory, the…
Langevin equations or generalized Langevin equations (GLEs) are popular models for describing the motion of a particle in a fluid medium in an effective manner. Here we examine particles immersed in an inherently nonequilibrium fluid, i.e.,…
A general Hamiltonian theory for the adiabatic motion of relativistic charged particles confined by slowly-varying background electromagnetic fields is presented based on a unified Lie-transform perturbation analysis in extended phase space…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
An asymmetric Brownian particle subjected to an external time-dependent force may acquire a net drift velocity, and thus operate as a motor or ratchet, even if the external force is represented by an unbiased time-periodic function or by a…
We study the biased diffusion of particles moving in one direction under the action of a constant force in the presence of a piecewise linear random potential. Using the overdamped equation of motion, we represent the first and second…
We address the problem of a microscopic derivation of the Langevin equation for a weakly relativistic Brownian particle. A non-covariant Hamiltonian model is adopted, in which the free motion of particles is described relativistically,…
We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum mechanical…
We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutator estimates, we gain the existence and uniqueness of…
Functionals of Brownian motion have diverse applications in physics, mathematics, and other fields. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger equation in…
We present a novel hybrid but thermodynamic approach to provide an alternative to the Langevin equation by using system-intrinsic (SI) microwork done by the Brownian particle in the kth microstate (realization). The corresponding…
We investigate solutions of backward stochastic differential equations (BSDE) with time delayed generators driven by Brownian motions and Poisson random measures, that constitute the two components of a Levy process. In this new type of…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
The aim of this paper is to present the new results concerning some functionals of Brownian motion with drift and present their applications in financial mathematics. We find a probabilistic representation of the Laplace transform of…
Generalizing Brownian motion (BM), fractional Brownian motion (FBM) is a paradigmatic selfsimilar model for anomalous diffusion. Specifically, varying its Hurst exponent, FBM spans: sub-diffusion, regular diffusion, and super-diffusion. As…