Add to ORKGAs a generalisation of Lamperti’s transformation, it has been proved by Alili, Chaumont, Grackzyk and Zak that a stable process in dimension d can be seen as the exponential of a Markov additive process (MAP) time changed. In this talk, we aim at describing the so called upward, respectively downward, ladder height processes associated to this MAP. We will provide a precise description in the case where d=1, and, in general, how the characteristics of this process could be derived from known identities for stable processes. This is based on a ongoing collaboration with Kyprianou, Satitkanitkul and Sengul.Non UBCUnreviewedAuthor affiliation: CIMAT A.C.Facult
We give a link between stochastic processes which are infinitely divisible with respect to time (IDT...
AbstractThe distribution of ladder variables is obtained for the class of processes with stationary ...
This thesis contains several results concerning alpha-stable processes, processes with alpha-stable ...
With a view to computing fluctuation identities related to stable processes, we review and extend th...
We show that if a Levy process creeps then, as a function of u, the renewal function V (t, u) of the...
We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we ...
We consider two first passage problems for stable processes, not necessarily symmetric, in one dimen...
Conditioning Markov processes to avoid a domain is a classical problem that has been studied in many...
For a positive self-similar Markov process, X, we construct a local time for the random set, Θ, of t...
Abstract. We apply dynamical ideas within probability theory, proving an almost-sure invariance prin...
In this paper, we consider a new family of Rd-valued Lévy processes that we call Lamperti stable. On...
A stochastically continuous process ξt, t≥­0, is said to be time-stable if the sum of n i....
A stepping stone model with site space a continuous, hierarchical group is constructed via duality w...
We study relations between P{supt[set membership, variant][0,h] [xi](t)>u} and for a stationary proc...
34 pages, 2 figuresIn the present work, we consider spectrally positive Lévy processes $(X_t,t\geq0)...
We give a link between stochastic processes which are infinitely divisible with respect to time (IDT...
AbstractThe distribution of ladder variables is obtained for the class of processes with stationary ...
This thesis contains several results concerning alpha-stable processes, processes with alpha-stable ...
With a view to computing fluctuation identities related to stable processes, we review and extend th...
We show that if a Levy process creeps then, as a function of u, the renewal function V (t, u) of the...
We give three applications of the Pecherskii-Rogozin-Spitzer identity for Lévy processes. First, we ...
We consider two first passage problems for stable processes, not necessarily symmetric, in one dimen...
Conditioning Markov processes to avoid a domain is a classical problem that has been studied in many...
For a positive self-similar Markov process, X, we construct a local time for the random set, Θ, of t...
Abstract. We apply dynamical ideas within probability theory, proving an almost-sure invariance prin...
In this paper, we consider a new family of Rd-valued Lévy processes that we call Lamperti stable. On...
A stochastically continuous process ξt, t≥­0, is said to be time-stable if the sum of n i....
A stepping stone model with site space a continuous, hierarchical group is constructed via duality w...
We study relations between P{supt[set membership, variant][0,h] [xi](t)>u} and for a stationary proc...
34 pages, 2 figuresIn the present work, we consider spectrally positive Lévy processes $(X_t,t\geq0)...
We give a link between stochastic processes which are infinitely divisible with respect to time (IDT...
AbstractThe distribution of ladder variables is obtained for the class of processes with stationary ...
This thesis contains several results concerning alpha-stable processes, processes with alpha-stable ...