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11 papers · 2 filters
Unbiased shifts of Brownian motion
Günter Last, Peter Mörters, Hermann Thorisson
Let be a two-sided standard Brownian motion. An unbiased shift of is a random time , which is a measurable function of , such that $(B_{T+t}…
Hitting distributions of alpha-stable processes via path censoring and self-similarity
Andreas E. Kyprianou, Alex Watson, Juan Carlos Pardo
In this paper we return to the problem of Blumenthal-Getoor-Ray, published in 1961, which gave the law of the position of first entry of a symmetric alpha-stable process into the u…
Minimal configurations and sandpile measures
Antal A. Jarai, Nicolas Werning
We give a new simple construction of the sandpile measure on an infinite graph G, under the sole assumption that each tree in the Wired Uniform Spanning Forest on G has one end alm…
An application of the backbone decomposition to supercritical super-Brownian motion with a barrier
A. Kyprianou, A. Murillo-Salas, J. L. Perez
We analyse the behaviour of supercritical super-Brownian motion with a barrier through the pathwise backbone embedding of Berestycki et al. (2011). In particular, by considering ex…
Optimal stopping problems for the maximum process with upper and lower caps
Curdin Ott
This paper concerns optimal stopping problems driven by the running maximum of a spectrally negative Lévy process . More precisely, we are interested in modifications of the She…
The theory of scale functions for spectrally negative Le vy processes
Alexey Kuznetsov, Andreas E. Kyprianou, Victor Rivero
The purpose of this review article is to give an up to date account of the theory and application of scale functions for spectrally negative Levy processes. Our review also include…