4 papers
Fluctuations of Discrete-Time Random Walks
Denis Denisov, Vitali Wachtel
These notes are devoted to fluctuations of one-dimensional random walks. We discuss various approaches to first-passage times and to the corresponding conditional distributions. Af…
Random walks in Weyl chambers
Denis Denisov, Will FitzGerald, Kaiyuan Zhang
We study a -dimensional random walk with zero mean and finite variance in the Weyl chambers of type C and D. Under optimal moment assumptions we construct positive harmonic func…
Markov chains in the domain of attraction of Brownian motion in cones
Denis Denisov, Kaiyuan Zhang
We consider a multidimensional Markov Chain converging to a multidimensional Brownian Motion. We construct a positive harmonic function for killed on exiting the cone. We s…
Tail asymptotics for the supremum of a random walk when the mean is not finite
D. Denisov, S. Foss, D. Korshunov
We consider the sums of independent identically distributed random variables. We do not assume that the 's have a finite mean. Under subexponential type con…