Related papers: Simultaneous boundary hitting by coupled reflected…
We construct obliquely reflected Brownian motions in all bounded simply connected planar domains, including non-smooth domains, with general reflection vector fields on the boundary. Conformal mappings and excursion theory are our main…
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 the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We…
The Brownian motion of a test particle interacting with a quantum scalar field in the presence of a perfectly reflecting boundary is studied in (1 + 1)-dimensional flat spacetime. Particularly, the expressions for dispersions in velocity…
In this paper we consider a (reflected) Brownian motion with broken drift hitting a random boundary. Some dedicated calculations allow us to obtain the formula on the joint Laplace transform of the hitting time and hitting position. These…
For every bounded planar domain $D$ with a smooth boundary, we define a `Lyapunov exponent' $\Lambda(D)$ using a fairly explicit formula. We consider two reflected Brownian motions in $D$, driven by the same Brownian motion (i.e., a…
Reflecting boundary conditions cause two one-dimensional random walks to synchronize if a common direction is chosen in each step. The mean synchronization time and its standard deviation are calculated analytically. Both quantities are…
The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a…
We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These…
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…
We consider an infinite system of non overlapping globules undergoing Brownian motions in R^3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is…
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 derive the asymptotic behavior of hitting probability at small target of size $O(\epsilon)$ for reflected Brownian motion in domains with suitable smooth boundary conditions, where the boundary of domain contains both reflecting part,…
Local perturbations of a Brownian motion are considered. As a limit we obtain a non-Markov process that behaves as a reflected Brownian motion on the positive half line until its local time at zero reaches some exponential level, then…
Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and (or) singular repellent drift. When the domain is a polyhedron, we prove that the…
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…
We state an exact simulation scheme for the first passage time of a Brownian motion to a symmetric linear boundary.
For a random walk defined for a doubly infinite sequence of times, we let the time parameter itself be an integer-valued process, and call the orginal process a random walk at random time. We find the scaling limit which generalizes the…
We introduce a system of Brownian particles, each absorbed upon hitting an associated moving boundary. The boundaries are determined by the conditional probabilities of the particles being absorbed before some final time horizon, given the…
We study a simple singular control problem for a Brownian motion with constant drift and variance reflected at the origin. Exerting control pushes the process towards the origin and generates a concave increasing state-dependent yield which…