Related papers: Feynman-Kac equation revisited
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and…
We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…
Anomalous transport is usually described either by models of continuous time random walks (CTRW) or, otherwise by fractional Fokker-Planck equations (FFPE). The asymptotic relation between properly scaled CTRW and fractional diffusion…
Coarse-grained Langevin-type effective field equations are derived for classical systems of particles. These equations include the effects of thermal fluctuation and dissipation which may arise from coupling to an external bath, as in the…
The classical dynamics in stationary potentials that are random both in space and time is studied. It can be intuitively understood with the help of Chirikov resonances that are central in the theory of Chaos, and explored quantitatively in…
Using the influence functional formalism we show how to derive a generalized Einstein equation in the form of a Langevin equation for the description of the backreaction of quantum fields and their fluctuations on the dynamics of curved…
The statistical approach is used to calculate the parton distribution functions (PDFs) of the nucleon. At first it is assumed that the partons are free particles and the light-front kinematic variables are employed to extract the Bjorken…
We use an effective Markovian description to study the long-time behaviour of a nonlinear second order Langevin equation with Gaussian noise. When dissipation is neglected, the energy of the system grows as with time a power-law with an…
Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We…
In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requiring the evaluation of the second derivative of the potential in addition…
Diffusion in nonhomogeneous media is described by a dynamical process driven by a general Levy noise and subordinated to a random time; the subordinator depends on the position. This problem is approximated by a multiplicative process…
The Fokker-Planck (FP) equation governs the evolution of densities for stochastic dynamics of physical systems, such as the Langevin dynamics and the Lorenz system. This work simulates FP equations through a mean field control (MFC)…
We explore properties the solution of Langevin equation when stochastic influence is orthogonal to velocity of a particle. Wiener's process can accept unlimited values. But for these equations, the attraction surfaces exist. For these…
L\'{e}vy walk is a practical model and has wide applications in various fields. Here we focus on the effect of an external constant force on the L\'{e}vy walk with the exponent of the power-law distributed flight time $\alpha\in(0,2)$. We…
One key issue in the probability density function (PDF) approach for disperse two-phase turbulent flows is to close the diffusion term in the phase space. This study aimed to derive a kinetic equation for particle dispersion in turbulent…
We derive exact Langevin-type equations governing quasispecies dynamics. The inherent multiplicative noise has both real and imaginary parts. The numerical simulation of the underlying complex stochastic partial differential equations is…
Continuous time random walks have random waiting times between particle jumps. We define the correlated continuous time random walks (CTRWs) that converge to fractional Pearson diffusions (fPDs). The jumps in these CTRWs are obtained from…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
The influence that intrinsic local density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the…