Palm theory for random time changes.
Perturbations ponctuelles d'évolutions : construction d'espaces stationnaires
Perturbing the hexagonal circle packing: a percolation perspective
We consider the hexagonal circle packing with radius and perturb it by letting the circles move as independent Brownian motions for time . It is shown that, for large enough , if is the point process given by the center of the circles at time , then, as , the critical radius for circles centered at to contain an infinite component converges to that of continuum percolation (which was shown – based on a Monte Carlo estimate – by Balister, Bollobás and Walters to be strictly bigger than...
Point le plus visité par un mouvement brownien avec dérive
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