相关论文: On Brownian flights

Consider branching Brownian motion in which we begin with one particle at the origin, particles independently move according to Brownian motion, and particles split into two at rate one. It is well-known that the right-most particle at time…

In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the expansion of Brownian motion in this polynomial basis are…

The large deviation function has been known for a long time in the literature for the displacement of the rightmost particle in a branching random walk (BRW), or in a branching Brownian motion (BBM). More recently a number of…

Transport phenomena in spatially periodic systems far from thermal equilibrium are considered. The main emphasize is put on directed transport in so-called Brownian motors (ratchets), i.e. a dissipative dynamics in the presence of thermal…

We consider a geometric rough path associated with a fractional Brownian motion with Hurst parameter $H\in]{1/4}, {1/2}[$. We give an approximation result in a modulus type distance, up to the second order, by means of a sequence of rough…

We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of…

Consider n non-intersecting Brownian motions on $\mathbb{R}$, depending on time $t \in [0,1]$, with $m_i$ particles forced to leave from $a_i$ at time $t=0$, $1\leq i\leq q$, and $n_j$ particles forced to end up at $b_j$ at time $t=1$,…

This paper provides yet another look at the mixed fractional Brownian motion (fBm), this time, from the spectral perspective. We derive an approximation for the eigenvalues of its covariance operator, asymptotically accurate up to the…

The purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane.

We consider a stochastic flow $\phi_t(x,\omega)$ in $\mathbb{R}^n$ with initial point $\phi_0(x,\omega)=x$, driven by a single $n$-dimensional Brownian motion, and with an outward radial drift of magnitude $\frac{…

We obtain the uniform convergence rate for the Gaussian fluctuation of the radial part of the Brownian motion on a hyperbolic space. We also show that this result is sharp if the dimension of the hyperbolic space is two or general odd. Our…

An analysis is presented of a Brownian particle moving on the half-line, subject to a restoring force proportional to its displacement and an absorbing boundary at the origin. When the initial displacement is large, the central moments of…

We show that with probability 1, the trace B[0,1] of Brownian motion in space, has positive capacity with respect to exactly the same kernels as the unit square. More precisely, the energy of occupation measure on B[0,1] in the kernel…

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The…

Let (B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t + \mu t) be a three-dimensional Brownian motion with drift \mu, starting at the origin. Then X_t = ||(B^{(1)}_t ;B^{(2)}_t ;B^{(3)}_t +\mu t)||, its distance from the starting point, is a diffusion with…

In this paper we define Brownian local time as the almost sure limit of the local times of a nested sequence of simple, symmetric random walks. The limit is jointly continuous in $(t,x)$. The rate of convergence is $n^{\frac14} (\log…

We investigate the sample path properties of Martin-L\"of random Brownian motion. We show (1) that many classical results which are known to hold almost surely hold for every Martin-L\"of random Brownian path, (2) that the effective…

The distribution of the first hitting time of a disc for the standard two dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform we give fairy detailed asymptotic estimates of its density…

Let $B = (B_t)_{t \in {\bf R}}$ be a symmetric Brownian motion, i.e. $(B_t)_{t \in {\bf R}_+}$ and $(B_{-t})_{t \in {\bf R}_+}$ are independent Brownian motions starting at $0$. Given $a \ge b>0$, we describe the law of the random set…

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…