Related papers: A Dynamical Theory of Markovian Diffusion
We study the dynamics of a Brownian motion with a diffusion coefficient which evolves stochastically. We first study this process in arbitrary dimensions and find the scaling form and the corresponding scaling function of the position…
The evolution of the spatial degrees of freedom of a photon propagating through atmospheric turbulence is treated as a non-Markovian process. Here, we derive and solve the evolution equation for this process. The turbulent medium is modeled…
We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…
We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…
Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The…
We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective…
We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.
The paper studies a non-linear transformation between Brownian martingales, which is given by the inverse of the pricing operator in the mathematical finance terminology. Subsequently, the solvability of systems of equations corresponding…
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…
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…
It is well-known that Brownian ratchets can exhibit current reversals, wherein the sign of the current switches as a function of the driving frequency. We introduce a spatial discretization of such a two-dimensional Brownian ratchet to…
While active matter physics has traditionally focused on particles with overdamped dynamics, recent years have seen an increase of experimental and theoretical work on active systems with inertia. This also leads to an increased need for…
Our Recent advancements in stochastic processes have illuminated a paradox associated with the Einstein model of Brownian motion. The model predicts an infinite propagation speed, conflicting with the second law of thermodynamics. The…
We present a theory for the steady-state dynamics of a two-dimensional system of spherically symmetric active Brownian particles. The derivation of the theory consists of two steps. First, we integrate out the self-propulsions and obtain a…
It is discussed the limitations of the widely used markovian approximation applied to model the turbulent refractive index in lightwave propagation. It is well-known the index is a passive scalar field. Thus, the actual knowledge about…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
A particle subjected to a fluctuating force originated from its interaction with an external quantum system undergoes quantum Brownian motion. This phenomenon is investigated in detail for the case of a particle confined by a harmonic…
Properties of transport of molecular motors are investigated. A simplified model based on the concept of Brownian ratchets is applied. We analyze a stochastic equation of motion by means of numerical methods. The transport is systematically…