Limit theorems for subcritical branching processes in random environment
Limit theorems for sums of dependent random vectors in [Book]
Limit Theorems for Sums of Partial Quotients of Continued Fractions.
Limit theorems for the canonical von Mises statistics with dependent data.
Limit theorems for the longest run.
Limit theorems for the process of exceedances in large populations.
Limit theorems for U-statistics indexed by a one dimensional random walk
Let be a -random walk and be a sequence of independent and identically distributed -valued random variables, independent of the random walk. Let be a measurable, symmetric function defined on with values in . We study the weak convergence of the sequence , with values in the set of right continuous real-valued functions with left limits, defined byStatistical applications are presented, in particular we prove a strong law of large numbers for -statistics indexed by a one-dimensional...
Limit theorems for U-statistics indexed by a one dimensional random walk
Let (Sn)n≥0 be a -random walk and be a sequence of independent and identically distributed -valued random variables, independent of the random walk. Let h be a measurable, symmetric function defined on with values in . We study the weak convergence of the sequence , with values in D[0,1] the set of right continuous real-valued functions with left limits, defined by Statistical applications are presented, in particular we prove a strong law of large numbers for U-statistics indexed by...
Limit theorems for vertex-reinforced jump processes on regular trees.
Limit theorems in free probability theory II
Based on an analytical approach to the definition of multiplicative free convolution on probability measures on the nonnegative line ℝ+ and on the unit circle we prove analogs of limit theorems for nonidentically distributed random variables in classical Probability Theory.
Limit theorems in the boundary hitting problem for a multidimensional random walk.
Limit theory for some positive stationary processes with infinite mean
We prove stable limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from nonintegrable observables over certain piecewise expanding maps. This is done by extending Darling–Kac theory to a suitable family of infinite measure preserving transformations.
Limites non tangentielles, limites browniennes en probabilité et limites semi-fines.
Limiting behavior of a diffusion in an asymptotically stable environment
Limiting behavior of the perturbed empirical distribution functions evaluated at -statistics for strongly mixing sequences of random variables.
Limiting behaviour of moving average processes based on a sequence of mixing and negatively associated random variables.
Limiting curlicue measures for theta sums
We consider the ensemble of curves {γα, N: α∈(0, 1], N∈ℕ} obtained by linearly interpolating the values of the normalized theta sum N−1/2∑n=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...
Limiting distribution for a simple model of order book dynamics
A continuous-time model for the limit order book dynamics is considered. The set of outstanding limit orders is modeled as a pair of random counting measures and the limiting distribution of this pair of measure-valued processes is obtained under suitable conditions on the model parameters. The limiting behavior of the bid-ask spread and the midpoint of the bid-ask interval are also characterized.
Limiting properties of the k-th record values
Limiting spectral distribution of circulant type matrices with dependent inputs.