Let X be a spectrally negative self-similar Markov process with 0 as an absorbing state. In
this paper, we show that the distribution of the absorption time is absolutely continuous with …

In this article we get simple formulas for Es≦tX(s) where X is a spectrally positive or
negative Lévy process with infinite variation. As a consequence we derive a generalization …

Bernyk et al.[Bernyk, V., Dalang, RC, Peskir, G., 2008. The law of the supremum of a stable
Lévy process with no negative jumps. Ann. Probab. 36, 1777–1789] offer a power series and …

Consider a spectrally one-sided Lévy process X and reflect it at its past infimum I. Call this
process Y. For spectrally positive X, Avram et al.(2) found an explicit expression for the law …

We start by providing an explicit characterization and analytical properties, including the
persistence phenomena, of the distribution of the extinction time TT of a class of non …

We consider some special classes of Lévy processes with no gaussian component whose
Lévy measure is of the type π (dx)= eγxν (ex− 1) dx, where ν is the density of the stable Lévy …

In this note we give, for a spectrally negative Lévy process, a compact formula for the
Parisian ruin probability, which is defined by the probability that the process exhibits an …

The aim of this note is to give a straightforward proof of a general version of the Ciesielski–
Taylor identity for positive self-similar Markov processes of the spectrally negative type …

Recurrent extensions of self-similar Markov processes and Cramer's condition II Page 1
Bernoulli 13(4), 2007, 1053–1070 DOI: 10.3150/07-BEJ6082 Recurrent extensions of self-similar …

A multiplicative identity in law connecting the hitting times of completely asymmetric α-stable
Lévy processes in duality is established. In the spectrally positive case, this identity allows …