Testing the independence of two Poisson processes.
The almost sure invariance principle for the empirical process of U-statistic structure
The brownian cactus I. Scaling limits of discrete cactuses
The cactus of a pointed graph is a discrete tree associated with this graph. Similarly, with every pointed geodesic metric space , one can associate an -tree called the continuous cactus of . We prove under general assumptions that the cactus of random planar maps distributed according to Boltzmann weights and conditioned to have a fixed large number of vertices converges in distribution to a limiting space called the Brownian cactus, in the Gromov–Hausdorff sense. Moreover, the Brownian cactus...
The functional central limit theorem for strongly mixing processes
The functional moderate deviations for Harris recurrent Markov chains and applications
The infinite Brownian loop on a symmetric space.
The invariance principle for nonstationary sequences of associated random variables
The law of large numbers and a functional equation
We deal with the linear functional equation (E) , where g:(0,∞) → (0,∞) is unknown, is a probability distribution, and ’s are positive numbers. The equation (or some equivalent forms) was considered earlier under different assumptions (cf. [1], [2], [4], [5] and [6]). Using Bernoulli’s Law of Large Numbers we prove that g has to be constant provided it has a limit at one end of the domain and is bounded at the other end.
The principle of large deviations for martingale additive functionals of recurrent Markov processes.
The quenched invariance principle for random walks in random environments admitting a bounded cycle representation
We derive a quenched invariance principle for random walks in random environments whose transition probabilities are defined in terms of weighted cycles of bounded length. To this end, we adapt the proof for random walks among random conductances by Sidoravicius and Sznitman (Probab. Theory Related Fields129 (2004) 219–244) to the non-reversible setting.
The Rate of Convergence in the Functional Central Limit Theorem for Random Quadratic Forms with Some Applications to the Law of Iterated Logarithm.
The rate of convergence of option prices when general martingale discrete-time scheme approximates the Black-Scholes model
We take the martingale central limit theorem that was established, together with the rate of convergence, by Liptser and Shiryaev, and adapt it to the multiplicative scheme of financial markets with discrete time that converge to the standard Black-Scholes model. The rate of convergence of put and call option prices is shown to be bounded by . To improve the rate of convergence, we suppose that the increments are independent and identically distributed (but without binomial or similar restrictions...
Théorème de la limite centrale et convergence fonctionnelle vers un processus à accroissements indépendants : la méthode des martingales
Théorème de limite centrale fonctionnel pour une chaîne de Markov récurrente au sens de Harris et positive
Théorèmes de limite centrale fonctionnels pour les processus de Markov
Théorèmes limite fonctionnels pour les processus de vraisemblance (cadre asymptotiquement non gaussien)
Tusnady's lemma, 24 years later
Two parameter extension of an observation of Poincaré
Two-dimensional Poisson trees converge to the brownian web