Related papers: Evaluation of the probability current in the stoch…
This review provides a pedagogic and self-contained introduction to master equations and to their representation by path integrals. We discuss analytical and numerical methods for the solution of master equations, keeping our focus on…
The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…
Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an…
Physical and chemical stochastic processes described by the master equation are investigated. In this paper, we examine the entropy production both for the master equation and for the corresponding Fokker-Planck equation. For the master…
Motivated by applications in systems biology, we seek a probabilistic framework based on Markov processes to represent intracellular processes. We review the formal relationships between different stochastic models referred to in the…
In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a double-well…
We consider particle transport under the influence of time-varying driving forces, where fluctuation relations connect the statistics of pairs of time reversed evolutions of physical observables. In many "mesoscopic" transport processes,…
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…
We formulate Bayesian updates in Markov processes by means of path integral techniques and derive the imaginary-time Schr\"{o}dinger equation with likelihood to direct the inference incorporated as a potential for the posterior probability…
We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a…
We propose a general method to identify nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) as gradient flows on the space of probability measures on $\mathbb{R}^d$ with a natural differential geometry. Our notion of gradient…
We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…
We present a new method to derive kinetic equations for systems undergoing non-linear transport in the presence of memory effects. In the framework of mesoscopic nonequilibrium thermodynamics, we derive a generalized Fokker-Planck equation…
Nonlinear Fokker-Planck equations play a major role in modeling large systems of interacting particles with a proved effectiveness in describing real world phenomena ranging from classical fields such as fluids and plasma to social and…
Probabilistic tractography based on diffusion weighted MRI has become a powerful approach for quantifying structural brain connectivities. In several works the similarity of probabilistic tractography and path integrals was already pointed…
This paper considers the Fokker-Planck equation and path integral formulation of the fractional Ornstein-Uhlenbeck process parametrized by two indices. The effective Fokker-Planck equation of this process is derived from the associated…
The time-integrated current of the TASEP has non-Gaussian fluctuations of order $t^{1/3}$. The recently discovered connection to random matrices and the Painlev\'e II Riemann-Hilbert problem provides a technique through which we obtain the…
We consider the single-file motion of colloidal particles interacting via short-ranged repulsion and placed in a traveling wave potential, that varies periodically in time and space. Under suitable driving conditions, a directed…
We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…
The stochastic theory of relativistic quantum mechanics presented here is modelled on the one that has been proposed previously and that was claimed to be a promising substitute to the orthodox theory in the non-relativistic domain. So it…