53 citations · 489 across the 66 of their papers we have counts for
6 papers · 1 filter
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…
A human proof of Gessel's lattice path conjecture
Alin Bostan, Irina Kurkova, Kilian Raschel
Gessel walks are lattice paths confined to the quarter plane that start at the origin and consist of unit steps going either West, East, South-West or North-East. In 2001, Ira Gess…
New steps in walks with small steps in the quarter plane
Irina Kurkova, Kilian Raschel
In this article we obtain new expressions for the generating functions counting (non-singular) walks with small steps in the quarter plane. Those are given in terms of infinite ser…
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…
Random walks in the quarter plane, discrete harmonic functions and conformal mappings
Kilian Raschel
We propose a new approach for finding discrete harmonic functions in the quarter plane with Dirichlet conditions. It is based on solving functional equations that are satisfied by…
Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0
Rim Essifi, Marc Peigné, Kilian Raschel
In this article we refine well-known results concerning the fluctuations of one-dimensional random walks. More precisely, if is a random walk starting from 0 and…