Asymptotics for random walks with dependent heavy-tailed increments.
Asymptotics for rooted bipartite planar maps and scaling limits of two-type spatial trees.
Asymptotics for the -deviation of the variance estimator under diffusion
We consider a diffusion process smoothed with (small) sampling parameter . As in Berzin, León and Ortega (2001), we consider a kernel estimate with window of a function of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the deviations such as
Asymptotics for the Lp-deviation of the variance estimator under diffusion
We consider a diffusion process Xt smoothed with (small) sampling parameter ε. As in Berzin, León and Ortega (2001), we consider a kernel estimate with window h(ε) of a function α of its variance. In order to exhibit global tests of hypothesis, we derive here central limit theorems for the Lp deviations such as
Asymptotics for the moment convergence of -statistics in LIL.
Asymptotics for the survival probability in a killed branching random walk
Consider a discrete-time one-dimensional supercritical branching random walk. We study the probability that there exists an infinite ray in the branching random walk that always lies above the line of slope γ − ε, where γ denotes the asymptotic speed of the right-most position in the branching random walk. Under mild general assumptions upon the distribution of the branching random walk, we prove that when ε → 0, this probability decays like exp{−(β+o(1)) / ε1/2}, where β is a positive constant...
Asymptotics of a dynamic random walk in a random scenery : I. Law of large numbers
Asymptotics of a generalized matrix renewal function.
Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations
This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...
Asymptotics of Bernoulli random walks, bridges, excursions and meanders with a given number of peaks.
Asymptotics of certain coagulation-fragmentation processes and invariant Poisson-Dirichlet measures.
Asymptotics of counts of small components in random structures and models of coagulation-fragmentation
We establish necessary and sufficient conditions for the convergence (in the sense of finite dimensional distributions) of multiplicative measures on the set of partitions. The multiplicative measures depict distributions of component spectra of random structures and also the equilibria of classic models of statistical mechanics and stochastic processes of coagulation-fragmentation. We show that the convergence of multiplicative measures is equivalent to the asymptotic independence of counts of...
Asymptotics of cross sections for convex bodies.
Asymptotics of permutations with nearly periodic patterns of rises and falls.
Asymptotics of riskless profit under selling of discrete time call options
A discrete time model of financial market is considered. In the focus of attention is the guaranteed profit of the investor which arises when the jumps of the stock price are bounded. The limit distribution of the profit as the model becomes closer to the classic model of geometrical Brownian motion is established. It is of interest that the approximating continuous time model does not assume any such profit.
Asymptotics of the allele frequency spectrum associated with the Bolthausen-Sznitman coalescent.
Asymptotics of the regression quantile basic solution under misspecification
We consider the asymptotic distribution of covariate values in the quantile regression basic solution under weak assumptions. A diagnostic procedure for assessing homogeneity of the conditional densities is also proposed.
Asymptotics of the stationary distribution of an oscillating random walk.
Asymptotics of variance of the lattice point count
The variance of the number of lattice points inside the dilated bounded set with random position in has asymptotics if the rotational average of the squared modulus of the Fourier transform of the set is . The asymptotics follow from Wiener’s Tauberian theorem.
Asymptotics of weighted empirical processes of linear fields with long-range dependence