Related papers: Two-dimensional Brownian motion with dependent com…
We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimensional operator process with monotone and antimonotone…
We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
We consider a Brownian particle moving on a ring. We study the probability distributions of the total number of turns and the net number of counter-clockwise turns the particle makes till time t. Using a method based on the renewal…
Brownian motion is essential for describing diffusion in systems ranging from simple to complex liquids. Unlike simple liquids, which consist of only a solvent, complex liquids, such as colloidal suspensions or the cytoplasm of a cell, are…
One century after Einstein's work, Brownian Motion still remains both a fundamental open issue and a continous source of inspiration for many areas of natural sciences. We first present a discussion about stochastic and deterministic…
Statistical physics courses typically employ abstract language that describes objects too small to be seen, making the topic challenging for students to understand. In this work, we introduce a simple experiment that allows conceptualizing…
This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian…
This work proposes a method for the two-dimensional simulation of Brownian particles in a fluid with restrictions. The method is based on simple numerical rules between two matrices. One of the matrix represent the identification of all…
Transport phenomena are ubiquitous in nature and known to be important for various scientific domains. Examples can be found in physics, electrochemistry, heterogeneous catalysis, physiology, etc. To obtain new information about diffusive…
In this paper, we develop a theory of common decomposition for two correlated Brownian motions, in which, by using change of time method, the correlated Brownian motions are represented by a triplet of processes, $(X,Y,T)$, where $X$ and…
Circular Dyson Brownian motion describes the Brownian dynamics of particles on a circle (periodic boundary conditions), interacting through a logarithmic, long-range two-body potential. Within the log-gas picture of random matrix theory, it…
This article is devoted to methods of construction and study of stochastic models based on Monte Carlo method. A model of Brownian motion, the construction and processing which brings to a world of random numbers and mathematical…
We consider processes which have the distribution of standard Brownian motion (in the forward direction of time) starting from random points on the trajectory which accumulate at $-\infty$. We show that these processes do not have to have…
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…
We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein-Uhlenbeck process for active speed generation. Using a…
With the rich dynamics studies of single-state processes, the two-state processes attract more and more interests of people, since they are widely observed in complex system and have effective applications in diverse fields, say, foraging…
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends…
In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called…
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…