Related papers: Fluid approach to two-sided Markov-modulated Brown…
We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective…
We study the asymptotic properties, in the weak sense, of regenerative processes and Markov renewal processes. For the latter, we derive both renewal-type results, also concerning the related counting process, and ergodic-type ones,…
We establish diffusion and fractional Brownian motion approximations for motions in a Markovian Gaussian random field with a nonzero mean.
We revisit the Markov approximation necessary to derive ordinary Brownian motion from a model widely adopted in literature for this specific purpose. We show that this leads to internal inconsistencies, thereby implying that further search…
Over a century ago, Einstein formulated a precise mathematical model for describing Brownian motion. While this model adequately explains the diffusion of micron-sized particles in fluids, its limitations become apparent when applied to…
We consider a Markovian approximation, of weak coupling type, to an open system perturbation involving emission, absorption and scattering by reservoir quanta. The result is the general form for a quantum stochastic flow driven by creation,…
Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation.…
We study fractional Brownian motion (fBm) characterized by the Hurst exponent H. Using a Monte Carlo sampling technique, we are able to numerically generate fBm processes with an absorbing boundary at the origin at discrete times for a…
In a previous paper, we established strong existence and uniqueness for a reflected diffusion $(X,S)$ with values in $\bar D\times \mathbbm{R}^p$, solving the following pair of stochastic differential equations: $$ dX_t = \sigma(X_t)dB_t +…
Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to math finance, and under general stability conditions, it has a unique stationary distribution.…
We study a system of reflected Brownian motions on the positive half-line in which each particle has a drift toward the origin determined by the local times at the origin of all the particles. If this local time drift is too strong, such…
This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time $t$ is…
Assume that a stochastic processes can be approximated, when some scale parameter gets large, by a fluid limit (also called "mean field limit", or "hydrodynamic limit"). A common practice, often called the "fixed point approximation"…
While Macroscopic Fluctuation Theory (MFT) has been highly successful in analyzing non-equilibrium steady states, its application to non-steady-state processes remains limited. In this study, we apply MFT to the relaxation process of…
We give necessary and sufficient conditions for the stationary density of semimartingale reflected Brownian motion in a wedge to be written as a finite sum of terms of exponential product form. Relying on geometric ideas reminiscent of the…
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--$\newrho$ model for irreversible…
For refracted skew Brownian motion (skew Brownian motion with two-valued drift), adopting a perturbation approach we find expressions of its potential densities. As applications, we recover its transition density and study its long-time…
We investigate yet another approach to understand the limit behaviour of Brownian motion conditioned to stay within a tubular neighbourhood around a closed and connected submanifold of a Riemannian manifold. In this context, we identify a…
We introduce numerical methods for simulating the diffusive motion of rigid bodies of arbitrary shape immersed in a viscous fluid. We parameterize the orientation of the bodies using normalized quaternions, which are numerically robust,…
In this work, we focus on the stationary analysis of a specific class of continuous time Markov-modulated reflected random walks in the quarter plane with applications in the modelling of two-node Markov-modulated queueing networks with…