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Changing the branching mechanism of a continuous state branching process using immigration

Romain Abraham, Jean-François Delmas (2009)

Annales de l'I.H.P. Probabilités et statistiques

We consider an initial population whose size evolves according to a continuous state branching process. Then we add to this process an immigration (with the same branching mechanism as the initial population), in such a way that the immigration rate is proportional to the whole population size. We prove this continuous state branching process with immigration proportional to its own size is itself a continuous state branching process. By considering the immigration as the apparition of a new type,...

Changing time for two-parameter strong martingales

D. Nualart, M. Sanz (1981)

Annales de l'I.H.P. Probabilités et statistiques

Chaos expansions and local times.

David Nualart, Josep Vives (1992)

Publicacions Matemàtiques

In this note we prove that the Local Time at zero for a multiparametric Wiener process belongs to the Sobolev space Dk - 1/2 - ε,2 for any ε > 0. We do this computing its Wiener chaos expansion. We see also that this expansion converges almost surely. Finally, using the same technique we prove similar results for a renormalized Local Time for the autointersections of a planar Brownian motion.

Chaotic behavior of infinitely divisible processes

S. Cambanis, K. Podgórski, A. Weron (1995)

Studia Mathematica

The hierarchy of chaotic properties of symmetric infinitely divisible stationary processes is studied in the language of their stochastic representation. The structure of the Musielak-Orlicz space in this representation is exploited here.

Chaoticity on a stochastic interval $[0, T]$

Azzouz Dermoune (1995)

Séminaire de probabilités de Strasbourg

Character theory of symmetric groups, analysis of long relators, and random walks.

Müller, Thomas W. (2006)

Séminaire Lotharingien de Combinatoire [electronic only]

Characterization of a regular family of semimartingales by line integrals.

Chitashvili, R., Mania, M. (1996)

Georgian Mathematical Journal

Characterization of equilibrium measures for critical reversible Nearest Particle Systems

Thomas Mountford, Li Wu (2008)

Open Mathematics

We show that for critical reversible attractive Nearest Particle Systems all equilibrium measures are convex combinations of the upper invariant equilibrium measure and the point mass at all zeros, provided the underlying renewal sequence possesses moments of order strictly greater than $\frac{7 + \sqrt{41}}{2}$ and obeys some natural regularity conditions.

Characterization of unitary processes with independent and stationary increments

Lingaraj Sahu, Kalyan B. Sinha (2010)

Annales de l'I.H.P. Probabilités et statistiques

This is a continuation of the earlier work (Publ. Res. Inst. Math. Sci.45 (2009) 745–785) to characterize unitary stationary independent increment gaussian processes. The earlier assumption of uniform continuity is replaced by weak continuity and with technical assumptions on the domain of the generator, unitary equivalence of the process to the solution of an appropriate Hudson–Parthasarathy equation is proved.

Characterizations of processes with stationary and independent increments under $G$ -expectation

Yongsheng Song (2013)

Annales de l'I.H.P. Probabilités et statistiques

Our purpose is to investigate properties for processes with stationary and independent increments under $G$ -expectation. As applications, we prove the martingale characterization of $G$ -Brownian motion and present a pathwise decomposition theorem for generalized $G$ -Brownian motion.