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4 papers · 2 filters
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 Sequential Empirical Central Limit Theorem for Multiple Mixing Processes with Application to B-Geometrically Ergodic Markov Chains
Herold Dehling, Olivier Durieu, Marco Tusche
We investigate the convergence in distribution of sequential empirical processes of dependent data indexed by a class of functions F. Our technique is suitable for processes that s…
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…