Temps local et balayage des semimartingales
Temps local et superchamp
Temps local pour les martingales à deux indices par rapport à sa variation quadratique
Temps locaux d'intersection et points multiples des processus de Lévy
Testing randomness of spatial point patterns with the Ripley statistic
Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley K-statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different...
The asymptotic behavior of fragmentation processes
The fragmentation processes considered in this work are self-similar Markov processes which are meant to describe the evolution of a mass that falls apart randomly as time passes. We investigate their pathwise asymptotic behavior as . In the so-called homogeneous case, we first point at a law of large numbers and a central limit theorem for (a modified version of) the empirical distribution of the fragments at time . These results are reminiscent of those of Asmussen and Kaplan [3] and Biggins...
The average density of super-brownian motion
The Azéma martingales as components of quantum independent increment processes
The Banach space of workable contingent claims in arbitrage theory
The best bounds in a theorem of Russell Lyons.
The best estimation of a ratio inequality for continuous martingales
The Beurling estimate for a class of random walks.
The Brownian fractional motion as a limit of some types of stochastic processes.
The central limit problem for strictly stationary sequences [Abstract of thesis]
The central limit theorem for random fields
The chain records.
The change of variables formula on Wiener space
The classic differential evolution algorithm and its convergence properties
Differential evolution algorithms represent an up to date and efficient way of solving complicated optimization tasks. In this article we concentrate on the ability of the differential evolution algorithms to attain the global minimum of the cost function. We demonstrate that although often declared as a global optimizer the classic differential evolution algorithm does not in general guarantee the convergence to the global minimum. To improve this weakness we design a simple modification of the...
The cluster size distribution for a forest-fire process on .
The convex minorant of the Cauchy process.