Related papers: Dyson's Brownian motions, intertwining and interla…
It is known that a full description of Brownian motion in the entire course of time should incorporate both kinetic and hydrodynamic effects, but a formula accounts for both effects has been established only in three dimension and only for…
Basic properties of Brownian motion are used to derive two results concerning birth-death chains. First, the probability of extinction is calculated. Second, sufficient conditions on the transition probabilities of a birth-death chain are…
Consider the following mechanism for the random evolution of a distribution of mass on the integer lattice ${\mathbf{Z}}$. At unit rate, independently for each site, the mass at the site is split into two parts by choosing a random…
We derive a family of series representations of the multiparameter fractional Brownian motion in the centred ball of radius $R$ in the $N$-dimensional space $\mathbb{R}^N$. Some known examples of series representations are shown to be the…
In an ensemble of non-interacting Brownian particles, a finite systematic average velocity may temporarily develop, even if it is zero initially. The effect originates from a small nonlinear correction to the dissipative force, causing the…
We study two Brownian particles in dimension $d=1$, diffusing under an interacting resetting mechanism to a fixed position. The particles are subject to a constant drift, which biases the Brownian particles toward each other. We derive the…
We offer an alternative viewpoint on Dyson's original paper regarding the application of Brownian motion to random matrix theory (RMT). In particular we show how one may use the same approach in order to study the stochastic motion in the…
A multidimensional Brownian motion with partial reflection on a hyperplane $S$ in the direction $qN+\alpha $, where $N$ is the conormal vector to the hyperplane and $q\in [-1,1], \alpha \in S$ are given parametres, is constructed and this…
We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional equation, which is reminiscent from equations arising in the…
A nonlinear theory of quantum Brownian motion in classical environment is developed based on a thermodynamically enhanced nonlinear Schrodinger equation. The latter is transformed via the Madelung transformation into a nonlinear quantum…
We study the Brownian motion of an assembly of mobile inclusions embedded in a fluid membrane. The motion includes the dispersal of the assembly, accompanied by the diffusion of its center of mass. Usually, the former process is much faster…
We consider a superprocess with coalescing Brownian spatial motion. We first prove a dual relationship between two systems of coalescing Brownian motions. In consequence we can express the Laplace functionals for the superprocess in terms…
In this paper we present a dynamical system to generate Brownian motion based on the Langevin equation without stochastic term and using fractional derivatives, i.e., a deterministic Brownian motion model is proposed. The stochastic process…
We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.
One-dimensional system of Brownian motions called Dyson's model is the particle system with long-range repulsive forces acting between any pair of particles, where the strength of force is $\beta/2$ times the inverse of particle distance.…
We derive some maximal inequalities for the bifractional Brownian motion using comparison theorems for Gaussian processes.
In this article we consider a Brownian motion with drift of the form \[dS_t=\mu_t dt+dB_t\qquadfor t\ge0,\] with a specific nontrivial $(\mu_t)_{t\geq0}$, predictable with respect to $\mathbb{F}^B$, the natural filtration of the Brownian…
We consider a Markov-modulated Brownian motion reflected to stay in a strip [0,B]. The stationary distribution of this process is known to have a simple form under some assumptions. We provide a short probabilistic argument leading to this…
The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a…
We develop a general framework for response theory in diffusion processes governed by Fokker-Planck equations, based on the notion of the Dissipation Function. Using the analytically solvable Brownian oscillator model, we derive exact…