Calcul stochastique non adapté par rapport à la mesure aléatoire de Poisson
Central limit theorem for Gibbsian U-statistics of facet processes
A special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic joint moments for interaction U-statistics are calculated and the central limit theorem is derived using the method of moments.
Changing the branching mechanism of a continuous state branching process using immigration
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,...
Coalescents with simultaneous multiple collisions.
Competing particle systems and the Ghirlanda-Guerra identities.
Competing particle systems evolving by I.I.D. Increments.
Completely asymmetric Lévy processes confined in a finite interval
Complex determinantal processes and noise.
Conditional Markov chains - construction and properties
In this paper we study finite state conditional Markov chains (CMCs). We give two examples of CMCs, one which admits intensity, and another one, which does not admit an intensity. We also give a sufficient condition under which a doubly stochastic Markov chain is a CMC. In addition we provide a method for construction of conditional Markov chains via change of measure.
Connected allocation to Poisson points in .
Construction of diffusion processes with Wentzell's boundary conditions by means of Poisson point processes of Brownian excursions
Construction of semimartingales from pieces by the method of excursion point processes
Contiguity and LAN-property of sequences of Poisson processes
Using the concept of Hellinger integrals, necessary and sufficient conditions are established for the contiguity of two sequences of distributions of Poisson point processes with an arbitrary state space. The distribution of logarithm of the likelihood ratio is shown to be infinitely divisible. The canonical measure is expressed in terms of the intensity measures. Necessary and sufficient conditions for the LAN-property are formulated in terms of the corresponding intensity measures.
Convergence of randomly oscillating point patterns to the Poisson point process
Oscillating point patterns are point processes derived from a locally finite set in a finite dimensional space by i.i.d. random oscillation of individual points. An upper and lower bound for the variation distance of the oscillating point pattern from the limit stationary Poisson process is established. As a consequence, the true order of the convergence rate in variation norm for the special case of isotropic Gaussian oscillations applied to the regular cubic net is found. To illustrate these theoretical...
Corners and records of the Poisson process in quadrant.