On quadratic stochastic processes.
On real zeros of random polynomials with hyperbolic elements.
On some properties of J-convex stochastic processes.
On the distribution of the supremum for stochastic processes
On the lower bound for the number of real roots of a random algebraic equation.
On the non-equivalence of two criteria of comparability of stationary point processes
On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...
On the supremum of random Dirichlet polynomials
We study the supremum of some random Dirichlet polynomials , where (εₙ) is a sequence of independent Rademacher random variables, the weights (dₙ) are multiplicative and 0 ≤ σ < 1/2. Particular attention is given to the polynomials , , P⁺(n) being the largest prime divisor of n. We obtain sharp upper and lower bounds for the supremum expectation that extend the optimal estimate of Halász-Queffélec, . The proofs are entirely based on methods of stochastic processes, in particular the metric...
On the variance of the number of real zeros of a random trigonometric polynomial.
On the zeroes of some random functions
On transformations of Wiener space.
On Weak Convergence of Stochastic Processes With Lusin Path Spaces.
On zeros of self-reciprocal random algebraic polynomials.
-variation de fonctions aléatoires. 1ère partie : séries de Rademacher
-variation de fonctions aléatoires. 2ième partie : processus à accroissements indépendants
Pathwise approximations of processes based on the fine structure of their filtrations
Performance of hedging strategies in interval models
For a proper assessment of risks associated with the trading of derivatives, the performance of hedging strategies should be evaluated not only in the context of the idealized model that has served as the basis of strategy development, but also in the context of other models. In this paper we consider the class of so-called interval models as a possible testing ground. In the context of such models the fair price of a derivative contract is not uniquely determined and we characterize the interval...
Probabilistic metric spaces constructed from stationary Markov chains.
Processus de points marqués et processus ramifiés
Processus et espaces de Banach invariants par réarrangement