15 citations · 29 across the 9 of their papers we have counts for
8 papers · 1 filter
Asymptotics of returns to the coordinate axes for conditioned planar simple random walks
Rodolphe Garbit, Kilian Raschel
In this paper we study the number of returns to the coordinate axes for two-dimensional nearest-neighbour random walks. While one-dimensional results on returns are classical, much…
Random walks with drift inside a pyramid: convergence rate for the survival probability
Rodolphe Garbit, Kilian Raschel
We consider multidimensional random walks in pyramids, which by definition are cones formed by finite intersections of half-spaces. The main object of interest is the survival prob…
On the exit time from an orthant for badly oriented random walks
Rodolphe Garbit
In a recent paper, K. Raschel and R. Garbit proved that the exponential decreasing rate of the probability that a random walk (with all exponential moments) stays in a -dimensio…
On the exit time from a cone for Brownian motion with drift
Rodolphe Garbit, Kilian Raschel
We investigate the tail distribution of the first exit time of Brownian motion with drift from a cone and find its exact asymptotics for a large class of cones. Our results show in…
On the exit time from a cone for random walks with drift
Rodolphe Garbit, Kilian Raschel
We compute the exponential decay of the probability that a given multi-dimensional random walk stays in a convex cone up to time , as goes to infinity. We show that the latt…
A central limit theorem for two-dimensional random walks in a cone
Rodolphe Garbit
We prove that a planar random walk with bounded increments and mean zero which is conditioned to stay in a cone converges weakly to the corresponding Brownian meander if and only i…