相关论文: Values of Brownian intersection exponents III: Two…

We study the distribution of the maximal height of the outermost path in the model of $N$ nonintersecting Brownian motions on the half-line as $N\to \infty$, showing that it converges in the proper scaling to the Tracy-Widom distribution…

Given a Brownian Motion $W$, in this paper we study the asymptotic behavior, as $\eps \to 0$, of the quadratic covariation between $f (\eps W)$ and $W$ in the case in which $f$ is not smooth. Among the main features discovered is that the…

We obtain results on both weak and almost sure asymptotic behaviour of power variations of a linear combination of independent Wiener process and fractional Brownian motion. These results are used to construct strongly consistent parameter…

We investigate a system of Brownian particles weakly bound by attractive parity-symmetric potentials that grow at large distances as $V(x) \sim |x|^\alpha$, with $0 < \alpha < 1$. The probability density function $P(x,t)$ at long times…

We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…

The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional…

In last passage percolation models lying in the KPZ universality class, long maximizing paths have a typical deviation from the linear interpolation of their endpoints governed by the two-thirds power of the interpolating distance. This…

We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results…

Let \ell be the projected intersection local time of two independent Brownian paths in R^d for d=2,3. We determine the lower tail of the random variable \ell(U), where U is the unit ball. The answer is given in terms of intersection…

We study extreme-value statistics of Brownian trajectories in one dimension. We define the maximum as the largest position to date and compare maxima of two particles undergoing independent Brownian motion. We focus on the probability P(t)…

In this paper, we study a two-point boundary value problem consisting of the heat equation on the open interval $(0,1)$ with boundary conditions which relate first and second spatial derivatives at the boundary points. Moreover, the unique…

We calculate the exact asymptotic survival probability, Q, of a one-dimensional Brownian particle, initially located located at the point x in (-L,L), in the presence of two moving absorbing boundaries located at \pm(L+ct). The result is…

The joint distribution of maximum increase and decrease for Brownian motion up to an independent exponential time is computed. This is achieved by decomposing the Brownian path at the hitting times of the infimum and the supremum before the…

We study the two-dimensional fractional Brownian motion with Hurst parameter $H>{1/2}$. In particular, we show, using stochastic calculus, that this process admits a skew-product decomposition and deduce from this representation some…

We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the…

Let \beta_k(n) be the number of self-intersections of order k, appropriately renormalized, for a mean zero random walk X_n in Z^2 with 2+\delta moments. On a suitable probability space we can construct X_n and a planar Brownian motion W_t…

Let $W_i=\{W_i(t), t\in \mathbb{R}_+\}, i=1,2$ be two Wiener processes and $W_3=\{W_3(\mathbf{t}), \mathbf{t}\in \mathbb{R}_+^2\}$ be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower…

Consider n non-intersecting particles on the real line (Dyson Brownian motions), all starting from the origin at time=0, and forced to return to x=0 at time=1. For large n, the average mean density of particles has its support, for each…

We consider the use of random walks as an approach to obtain connection coefficients for higher-order Bernoulli and Euler polynomials. In particular, we consider the cases of a $1$-dimensional linear reflected Brownian motion and of a…

We introduce and study a noncommutative two-parameter family of noncommutative Brownian motions in the free Fock space. They are associated with Kesten laws and give a continuous interpolation between Brownian motions in free probability…