相关论文: Principal Eigenvalue for Brownian Motion on a Boun…

Let $D\subset R^d$ be a bounded domain and let $\mathcal P(D)$ denote the space of probability measures on $D$. Consider a Brownian motion in $D$ which is killed at the boundary and which, while alive, jumps instantaneously according to a…

We consider the degenerate Einstein's Brownian motion model for the case when the time interval ($\tau$) of particle Jumps before collision (free jumps) reciprocal to the number of particles per unit volume $u(x,t) > 0$ at the point of…

We consider the degenerate Einsteins Brownian motion model when the time interval of the moving particles before the collisions, is reciprocal to the number of particles per unit volume u(x,t), at the point of observation x at time t. The…

We derive explicit formulas for probabilities of Brownian motion with jumps crossing linear or piecewise linear boundaries in any finite interval. We then use these formulas to approximate the boundary crossing probabilities for general…

Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…

Let $(\tau_x)_{x \in \Z^d}$ be i.i.d. random variables with heavy (polynomial) tails. Given $a \in [0,1]$, we consider the Markov process defined by the jump rates $\omega_{x \to y} = {\tau_x}^{-(1-a)} {\tau_y}^a$ between two neighbours $x$…

We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $d=2$,…

We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other's path. Also, owing to the exact integrability of the level…

In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one-dimensional case. Our methods are different and mainly…

Throughout physics Brownian dynamics are used to describe the behaviour of molecular systems. When the Brownian particle is confined to a bounded domain, a particularly important question arises around determining how long it takes the…

We study the maximum of a Brownian motion with a parabolic drift; this is a random variable that often occurs as a limit of the maximum of discrete processes whose expectations have a maximum at an interior point. We give series expansions…

The logarithmic correction for the order of the maximum of a two-type reducible branching Brownian motion on the real line exhibits a double jump when the parameters (the ratio of the diffusion coefficients of the two types of particles,…

We establish an invariance principle connecting boundary random walks on $\mathbb N$ with Feller's Brownian motions on $[0,\infty)$. A Feller's Brownian motion is a Feller process on $[0,\infty)$ whose excursions away from the boundary $0$…

We prove a boundary Harnack inequality for jump-type Markov processes on metric measure state spaces, under comparability estimates of the jump kernel and Urysohn-type property of the domain of the generator of the process. The result holds…

We considered the qualitative behavior of the generalization of Einstein's model of Brownian motion when the key parameter of the time interval of \textit{free jump} degenerates. Fluids will be characterized by the number of particles per…

We consider the limit behavior of a one-dimensional random walk with unit jumps whose transition probabilities are modified every time the walk hits zero. The invariance principle is proved in the scheme of series where the size of…

Consider a two-type reducible branching Brownian motion in which particles' diffusion coefficients and branching rates are influenced by their types. Here reducible means that type 1 particles can produce particles of type 1 and type 2, but…

The first-passage-time problem for a Brownian motion with alternating infinitesimal moments through a constant boundary is considered under the assumption that the time intervals between consecutive changes of these moments are described by…

In this paper, we consider a linear model with jumps driven by a Brownian motion and a compensated Poisson process, whose drift and diffusion coefficients as well as its intensity are unknown parameters. Supposing that the process is…

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…