Related papers: Simulation of Reflected Brownian motion on two dim…

Prompted by an example arising in critical percolation, we study some reflected Brownian motions in symmetric planar domains and show that they are intertwined with one-dimensional diffusions. In the case of a wedge, the reflected Brownian…

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…

We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…

We study a model for the entanglement of a two-dimensional reflecting Brownian motion in a bounded region divided into two halves by a wall with three or more small windows. We map the Brownian motion into a Markov Chain on the fundamental…

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson…

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…

We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide necessary and sufficient conditions for existence and uniqueness of a solution to the corresponding submartingale problem…

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,…

Consider a generic triangle in the upper half of the complex plane with one side on the real line. This paper presents a tailored construction of a discrete random walk whose continuum limit is a Brownian motion in the triangle, reflected…

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…

Geometrical optics provides an instructive insight into Brownian motion, ``pushed" into a large-deviations regime by imposed constraints. Here we extend geometrical optics of Brownian motion by accounting for diffusion inhomogeneity in…

Fractional Brownian motion (FBM), a non-Markovian self-similar Gaussian stochastic process with long-ranged correlations, represents a widely applied, paradigmatic mathematical model of anomalous diffusion. We report the results of…

A uniform dimensional result for normally reflected Brownian motion (RBM) in a large class of non-smooth domains is established. Exact Hausdorff dimensions for the boundary occupation time and the boundary trace of RBM are given. Extensions…

We consider a Brownian motion forced to stay in the quadrant by an electrostatic oblique repulsion from the sides. We tackle the question of hitting the corner or an edge, and find product-form stationary measures under a certain condition,…

Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…

For Brownian motion in a (two-dimensional) wedge with negative drift and oblique reflection on the axes, we derive an explicit formula for the Laplace transform of its stationary distribution (when it exists), in terms of Cauchy integrals…

We consider several critical wetting models. In the discrete case, these probability laws are known to converge, after an appropriate rescaling, to the law of a reflecting Brownian motion, or of the modulus of a Brownian bridge, according…

We consider a transient Brownian motion reflected obliquely in a two-dimensional wedge. A precise asymptotic expansion of Green's functions is found in all directions. To this end, we first determine a kernel functional equation connecting…

Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in R^2 is given in polar coordinates by S={(r,theta): r >= 0, 0 <= theta <= xi} for some 0 < xi < 2 pi. Let alpha= (theta_1+theta_2)/xi,…

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the…