V́ıctor Rivero

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Let ξ be a real valued Lévy process that drifts to −∞ and satisfies Cramer's condition, and X a self–similar Markov process associated to ξ via Lamperti's [22] transformation. In this case, X has 0 as a trap and fulfills the assumptions of Vuolle-Apiala [34]. We deduce from [34] that there exists a unique excursion measure n, compatible with the semigroup(More)
We continue the recent work of [2] and [25] by showing that whenever the Lévy measure of a spectrally negative Lévy process has a density which is log convex then the solution of the associated actuarial control problem of de Finetti is solved by a barrier strategy. Moreover, the level of the barrier can be identified in terms of the scale function of the(More)
We consider increasing self–similar Markov processes (X t , t ≥ 0) on ]0, ∞[. By using the Lamperti's bijection between self–similar Markov processes and Lévy processes, we determine the functions f for which there exists a constant c ∈ R + \{0} such that lim inf t→∞ X t /f (t) = c with probability 1. The determination of such functions depends on the(More)
The Clinician Administered PTSD Scale was employed with 76 traumatized Dutch subjects from different treatment centers and one social rehabilitation center. Subjects were traumatized either in childhood, in adolescence, or in early adulthood. The CAPS showed an overall agreement with clinical diagnosis of 79%, with a kappa coefficient of .58. Interrater(More)
In this paper we obtain a Lamperti type representation for real-valued self-similar Markov processes, killed at their hitting time of zero. Namely, we represent real-valued self-similar Markov processes as time changed multiplicative invariant processes. Doing so, we complete Kiu's work [9], following some ideas in [7] in order to characterize the(More)
We discuss the existence and characterization of quasi-stationary distributions and Yaglom limits of self-similar Markov processes that reach 0 in finite time. By Yaglom limit, we mean the existence of a deterministic function g and a non-trivial probability measure ν such that the process rescaled by g and conditioned on non-extinction converges in(More)
In this study a newly developed Self-rating Inventory for Posttraumatic Stress Disorder (PTSD) is presented. The instrument consists of 47 items, reflecting DSM-III-R criteria, associated features and items corresponding to the disorder of extreme stress not otherwise specified. All items are phrased in a trauma-independent way and are measured on an(More)
Understanding the space–time features of how a Lévy process crosses a constant barrier for the first time, and indeed the last time, is a problem which is central to many models in applied probability such as queueing theory, financial and actuarial mathematics, optimal stopping problems, the theory of branching processes, to name but a few. In Doney and(More)
In this paper, we study the existence of the density associated to the exponential functional of the Lévy process ξ, I eq := eq 0 e ξs ds, where e q is an independent exponential r.v. with parameter q ≥ 0. In the case when ξ is the negative of a subordinator, we prove that the density of I eq , here denoted by k, satisfies an integral equation that(More)
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