相关论文: Synchronous couplings of reflected Brownian motion…

The Lie groups $SU(2)$ and $SL(2,\mathbb{R})$ can be viewed as model spaces in subRiemannian geometry. Coupling two subelliptic Brownian motions on $SU(2)$ (resp. $SL(2,\mathbb{R})$) consists in coupling two Brownian motions on the sphere…

The Dyson Brownian Motion (DBM) describes the stochastic evolution of $N$ points on the line driven by an applied potential, a Coulombic repulsion and identical, independent Brownian forcing at each point. We use an explicit tamed Euler…

It has been shown by various authors that the diameter of a given nontrivial bounded connected set $\mathcal{X}$ grows linearly in time under the action of an isotropic Brownian flow (IBF), which has a nonnegative top-Lyapunov exponent. In…

We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…

We study a Brownian motion with drift in a wedge of angle $\beta$ which is obliquely reflected on each edge along angles $\varepsilon$ and $\delta$. We assume that the classical parameter $\alpha=\frac{\delta+\varepsilon - \pi}{\beta}$ is…

Let $\tau_{D}(Z) $ is the first exit time of iterated Brownian motion from a domain $D \subset \RR{R}^{n}$ started at $z\in D$ and let $P_{z}[\tau_{D}(Z) >t]$ be its distribution. In this paper we establish the exact asymptotics of…

We consider a branching Brownian motion in $\mathbb{R}^d$. We prove that there exists a random subset $\Theta$ of $\mathbb{S}^{d-1}$ such that the limit of the derivative martingale exists simultaneously for all directions $\theta \in…

For each $m\ge 1$ and $p>2$ we characterize bounded simply connected Sobolev $L^m_p$-extension domains $\Omega\subset R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $\Omega$. Its proof is based on a…

We prove existence and uniqueness for semimartingale reflecting diffusions in 2-dimensional piecewise smooth domains with varying, oblique directions of reflection on each "side", under geometric, easily verifiable conditions. Our…

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…

Let $R:(0,\infty) \to [0,\infty)$ be a measurable function. Consider coalescing Brownian motions started from every point in the subset $\{ (0,x) : x \in \mathbb{R} \}$ of $[0,\infty) \times \mathbb{R}$ (with $[0,\infty)$ denoting time and…

We derive a three-term asymptotic expansion for the expected lifetime of Brownian motion and for the torsional rigidity on thin domains in R^n, and a two-term expansion for the maximum (and corresponding maximizer) of the expected lifetime.…

Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, non-linear feedback control. Specifically, the particle is subject to a force derived from…

By tracking the divergence of two initially close trajectories in phase space in an Eulerian approach to forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$, and the Reynolds number $Re$ is measured using direct…

Using the lookdown construction of Donnelly and Kurtz we prove that, at any fixed positive time, the $\Lambda$-Fleming-Viot process with underlying Brownian motion has a compact support provided that the corresponding $\Lambda$-coalescent…

We apply a Lyapunov function to obtain conditions for the existence and uniqueness of small classical time-periodic solutions to first order quasilinear 1D hyperbolic systems with (nonlinear) nonlocal boundary conditions in a strip. The…

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer…

It is proved that on any smoothly bounded domain $D$ in $\mathbb{R}^n$, $n>1$, the output of the harmonic Bergman projection belongs to the Sobolev space of order $k$ whenever all tangential derivatives of order up to k of the input…

We consider the model space of constant curvature in dimension n and characterize all co-adapted couplings of Brownian motions on this space for which the distance between the processes is deterministic. In addition, the construction of the…

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results…