30 citations · 75 across the 5 of their papers we have counts for
5 papers · 1 filter
Invariance principles for local times at the supremum of random walks and Lévy processes
Loïc Chaumont, Ron Arthur Doney
We prove that when a sequence of Lévy processes or a normed sequence of random walks converges a.s. on the Skorokhod space toward a Lévy process , the sequen…
Curve crossing for random walks reflected at their maximum
Ron Doney, Ross Maller
Let be a random walk reflected in its maximum. Except in the trivial case when , will pass over a horizontal boundary of a…
Passage of Lévy Processes across Power Law Boundaries at Small Times
Jean Bertoin, Ronald A. Doney, Ross A. Maller
We wish to characterise when a Lévy process crosses boundaries like , , in a one or two-sided sense, for small times ; thus, we enquire when $\limsup_{t\downarro…
Cramer's estimate for a reflected Levy process
R. A. Doney, R. A. Maller
The natural analogue for a Levy process of Cramer's estimate for a reflected random walk is a statement about the exponential rate of decay of the tail of the characteristic measur…
Stochastic bounds for Levy processes
R. A. Doney
Using the Wiener-Hopf factorization, it is shown that it is possible to bound the path of an arbitrary Levy process above and below by the paths of two random walks. These walks ha…