Related papers: Markov-modulated Brownian motion with two reflecti…
It has been shown that a nonvibrated magnetic granular system, when it is feeded by means an altenating magnetic field, behaves with most of the distinctive physical features of active matter systems. In this work we focus our attention on…
We present an interesting connection between Brownian motion and magnetism. We use this to determine the distribution of areas enclosed by the path of a particle diffusing on a sphere. In addition, we find a bound on the free energy of an…
We introduce a transient reflected Brownian motion in a multidimensional orthant, which is either absorbed at the apex of the cone or escapes to infinity. We address the question of computing the absorption probability, as a function of the…
We suggest a governing equation which describes the process of polymer chain translocation through a narrow pore and reconciles the seemingly contradictory features of such dynamics: (i) a Gaussian probability distribution of the…
Brownian motion whose infinitesimal variance changes according to a three-state continuous time Markov Chain is studied. This Markov Chain can be viewed as a telegraph process with one on state and two off states. We first derive the…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…
We ascertain the diffusively scaled limit of a periodic Lorentz process in a strip with an almost reflecting wall at the origin. Here, almost reflecting means that the wall contains a small hole waning in time. The limiting process is a…
We adapt ideas and concepts developed in optimal transport (and its martingale variant) to give a geometric description of optimal stopping times of Brownian motion subject to the constraint that the distribution of the stopping time is a…
We consider a simple but important class of metastable discrete time Markov chains, which we call perturbed Markov chains. Basically, we assume that the transition matrices depend on a parameter $\varepsilon$, and converge as $\varepsilon$.…
In this paper we prove matching upper and lower bounds for the transition density function of the subordinate reflected Brownian motion on fractals.
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…
We analyze the convergence to equilibrium of one-dimensional reflected Brownian motion (RBM) and compute a number of related initial transient formulae. These formulae are of interest as approximations to the initial transient for queueing…
Generalizations of tempered fractional Brownian from single index to two indices and variable index or tempered multifractional Brownian motion are studied. Tempered fractional Brownian motion and tempered multifractional Brownian motion…
Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection and the so-called submartingale problem. We introduce a general formulation of the submartingale problem for…
We use reflecting Brownian motion (RBM) to prove the well known Gauss-Bonnet-Chern theorem for a compact Riemannian manifold with boundary. The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary…
We prove the existence and uniqueness of a strong solution of a stochastic differential equation with normal reflection representing the random motion of finitely many globules. Each globule is a sphere with time-dependent random radius and…
Many economic models feature monotone Markov dynamics on state spaces that may be noncompact. Establishing existence, uniqueness, and stability of stationary distributions in such settings has required a patchwork of sufficient conditions,…
We give sharp two-sided estimates for the functions $g_M(t,x,y)$ and $g_M(t,x,y)-g(t,x,y)$, where $g_M(t,x,y)$ are the transition probability densities of the reflected Brownian motion on a $M$-complex of size $M \in \mathbb{Z}$ of an…
Let $\xi$ n , n $\in$ N be a sequence of i.i.d. random variables with values in Z. The associated random walk on Z is S(n) = $\xi$ 1 + $\times$ $\times$ $\times$ + $\xi$ n+1 and the corresponding "reflected walk" on N 0 is the Markov chain…