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 consider increasing self–similar Markov processes (Xt, 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 inft→∞Xt/f(t) = c with probability 1. The determination of such functions depends on the subordinator ξ(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 selfsimilar 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 underlying(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)
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)
Let P = (Px, x ≥ 0) be a family of probability measures on Skohorod’s space D , the space of càdlàg paths defined on [0,∞[ with values in R. The space D is endowed with the Skohorod topology and its Borel σ-field. We will denote by X the canonical process of the coordinates and (Gt, t≥ 0) will be the natural filtration generated by X . Assume that under P(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)
OBJECTIVE Miliary tuberculosis (MTB) is difficult to diagnose. When prompt diagnosis is necessary, the polymerase chain reaction (PCR) to detect mycobacterial DNA may be valuable. SETTING Tuberculosis clinic in an academic tertiary-level hospital in Mexico. DESIGN Bone marrow (BM) aspiration samples from 30 consecutive clinically suspected MTB patients(More)
To establish the frequency of infectious aetiology in Mexican adult patients with cervical lymphadenopathies (CLAs), 87 consecutive patients with enlarged cervical lymphatic nodes, HIV negative and without anti-tuberculous treatment, were selected from a tertiary-level speciality concentration hospital. Histopathological studies, investigation of acid-fast(More)
In this paper, we study the existence of the density associated to the exponential functional of the Lévy process ξ, Ieq := ∫ eq 0 es ds, where eq 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 Ieq , here denoted by k, satisfies an integral equation that generalizes(More)