Cerf, Raphaël Dembin, Barbara

We consider the anchored isoperimetric profile of the infinite open cluster, defined for p > p_c, whose existence has been recently proved in [3]. We extend adequately the definition for p = p_c, in finite boxes. We prove a partial result which implies that, if the limit defining the anchored isoperimetric profile at pc exists, it has to vanish.

Ngo, Hoang-Long Peigné, Marc

Let ξ n , n ∈ N be a sequence of i.i.d. random variables with values in Z. The associated random walk on Z is S(n) = ξ 1 + · · · + ξ n+1 and the corresponding "reflected walk" on N 0 is the Markov chain X(n), n ∈ N, given by X(0) = x ∈ N 0 and X(n + 1) = |X(n) + ξ n+1 | for n ≥ 0. It is well know that the reflected walk (X(n)) n≥0 is null-recurrent...

Ngo, Hoang-Long Peigné, Marc

We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at 0 whenever they cross that point. We show that the perturbed random walk, after being rescaled in a proper way, converges to a skew Brownian motion whose parameter is defined by renewal functions o...

Lakner, P. (Peter) Reed, J. (Josh) Zwart, A.P. (Bert)

Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in ℝ2 is given in polar coordinates by S = {(r, θ) : r ≥ 0, 0 ≤ θ ≤ ξ } for some 0 α, the strong p-variation of the sample paths of Y is finite on compact intervals, and, for 0

Lagnoux, Agnes Mercier, Sabine Vallois, Pierre

We calculate the probability density function of the local score position on complete excursions of a reflected Brownian motion. We use the trajecto-rial decomposition of the standard Brownian bridge to derive two different expressions of the density: the first one is based on a series and an integral while the second one is free off the series.

Hanks, Ephraim M. Johnson, Devin S. Hooten, Mevin B.
Published in
Journal of Agricultural, Biological and Environmental Statistics

Movement for many animal species is constrained in space by barriers such as rivers, shorelines, or impassable cliffs. We develop an approach for modeling animal movement constrained in space by considering a class of constrained stochastic processes, reflected stochastic differential equations. Our approach generalizes existing methods for modelin...

Arnaudon, Marc Li, Xue-Mei

We construct a family of SDEs whose solutions select a reflected Brownian flow as well as a stochastic damped transport process (W_t). The latter gives a representation for the solutions to the heat equation for differential 1-forms with the absolute boundary conditions; it evolves pathwise by the Ricci curvature in the interior, by the shape opera...

Batakis, Athanasios Nguyen, Viet Hung
Published in
Potential Analysis

We show that the dimension of the exit distribution of planar partially reflected Brownian motion can be arbitrarily close to 2.

Lange, Rutger-Jan

This thesis consists of three self-contained parts, each with its own abstract, body, references and page numbering. Part I, "Potential theory, path integrals and the Laplacian of the indicator", finds the transition density of absorbed or reflected Brownian motion in a d-dimensional domain as a Feynman-Kac functional involving the Laplacian of the...

Demni, Nizar Lépingle, Dominique

In the setting of finite reflection groups, we prove that the projection of a Brownian motion onto a closed Weyl chamber is another Brownian motion normally reflected on the walls of the chamber. Our proof is probabilistic and the decomposition we obtain may be seen as a multidimensional extension of Tanaka's formula for linear Brownian motion. The...