A Hájek-Rényi type inequality and its applications.
A Hájek-Rényi-type maximal inequality and strong laws of large numbers for multidimensional arrays.
A Hölderian FCLT for some multiparameter summation process of independent non-identically distributed random variables.
A large deviation result for the subcritical Bernoulli percolation
A large deviation theorem for the empirical eigenvalue distribution of random unitary matrices
A Law of the Iterated Logarithm for a Class of Polynomial Hypergroups.
A law of the iterated logarithm for general lacunary series
We prove a law of the iterated logarithm for sums of the form where the satisfy a Hadamard gap condition. Here we assume that f is a Dini continuous function on ℝⁿ which has the property that for every cube Q of sidelength 1 with corners in the lattice ℤⁿ, f vanishes on ∂Q and has mean value zero on Q.
A law of the iterated logarithm for the sample covariance matrix.
A limit law for the root value of minimax trees.
A limit theorem for functionals of a Poisson process
A limit theorem for joint distribution of order-statistics from stationary Gaussian sequences
A limit theorem for maxima of nonstationary Gaussian sequences
A limit theorem for the moment of self-normalized sums.
A limit theorem for the position of a particle in the Lorentz model.
A limit theorem for the q-convolution
The q-convolution is a measure-preserving transformation which originates from non-commutative probability, but can also be treated as a one-parameter deformation of the classical convolution. We show that its commutative aspect is further certified by the fact that the q-convolution satisfies all of the conditions of the generalized convolution (in the sense of Urbanik). The last condition of Urbanik's definition, the law of large numbers, is the crucial part to be proved and the non-commutative...
A limit theorem for the Riemann zeta-function in the complex space
A limit theorem for the Riemann zeta-function near the critical line in the complex space
A local convergence theorem for partial sums of stochastic adapted sequences
In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary information source, which is an extension of case of nonhomogeneous Markov chains.
A Local Limit Theorem for Attraction to the Standard Normal Law: The Case of Infinitive Variance.
A local limit theorem for directed polymers in random media : the continuous and the discrete case