Point processes of minimal order statistics
Point shift characterization of Palm measures on abelian groups.
Poisson convergence for the largest eigenvalues of heavy tailed random matrices
We study the statistics of the largest eigenvalues of real symmetric and sample covariance matrices when the entries are heavy tailed. Extending the result obtained by Soshnikov in (Electron. Commun. Probab.9 (2004) 82–91), we prove that, in the absence of the fourth moment, the asymptotic behavior of the top eigenvalues is determined by the behavior of the largest entries of the matrix.
Poisson matching
Suppose that red and blue points occur as independent homogeneous Poisson processes in ℝd. We investigate translation-invariant schemes for perfectly matching the red points to the blue points. For any such scheme in dimensions d=1, 2, the matching distance X from a typical point to its partner must have infinite d/2th moment, while in dimensions d≥3 there exist schemes where X has finite exponential moments. The Gale–Shapley stable marriage is one natural matching scheme, obtained by iteratively...
Poisson point process limits in size-biased Galton-Watson trees.
Poisson point processes attached to symmetric diffusions
Poisson thinning by monotone factors.
Poissonian products of random weights: uniform convergence and related measures.
Pricing of zero-coupon and coupon cat bonds
We apply the results of Baryshnikov, Mayo and Taylor (1998) to calculate non-arbitrage prices of a zero-coupon and coupon CAT bond. First, we derive pricing formulae in the compound doubly stochastic Poisson model framework. Next, we study 10-year catastrophe loss data provided by Property Claim Services and calibrate the pricing model. Finally, we illustrate the values of the CAT bonds tied to the loss data.
Pricing variance swaps for stochastic volatilities with delay and jumps.
Probabilités de présence dans un processus de branchement spatial markovien
Process-level large deviations for nonlinear Hawkes point processes
In this paper, we prove a process-level, also known as level-3 large deviation principle for a very general class of simple point processes, i.e. nonlinear Hawkes process, with a rate function given by the process-level entropy, which has an explicit formula.
Processus ponctuels binomiaux négatifs
Processus ponctuels marqués stochastiques. Représentation des martingales et filtration naturelle quasicontinue à gauche
Processus ponctuels stationnaires asymptotiquement gaussiens et comportement asymptotique de processus de branchement spatiaux sur-critiques
Quelques remarques sur un nouveau type d'équations différentielles stochastiques
Quermass-interaction process with convex compact grains
The paper concerns an extension of random disc Quermass-interaction process, i.e. the model of discs with mutual interactions, to the process of interacting objects of more general shapes. Based on the results for the random disc process and the process with polygonal grains, theoretical results for the generalized process are derived. Further, a simulation method, its advantages and the corresponding complications are described, and some examples are introduced. Finally, a short comparison to the...
Recouvrements aléatoires et théorie du potentiel
Recurrence and transience for long-range reversible random walks on a random point process.
Regenerative renewal processes