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Exact slopes of the rank statistics for the two-sample case under discrete distributions

Dana Vorlíčková (1981)

Aplikace matematiky

The author studies the linear rank statistics for testing the pypothesis of randomness against the alternative of two samples provided both are drawn grom discrete (integer-valued) distributions. The weak law of large numbers and the exact slope are obtained for statistics with randomized ranks of with averaged scores.

Existence and asymptotic behaviour of some time-inhomogeneous diffusions

Mihai Gradinaru, Yoann Offret (2013)

Annales de l'I.H.P. Probabilités et statistiques

Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient ρ sgn ( x ) | x | α / t β . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters ρ , α and β , of the recurrence, transience and convergence. More precisely, asymptotic...

Exponential deficiency of convolutions of densities

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

If a probability density p(x) (x ∈ ℝk) is bounded and R(t) := ∫e〈x, tu〉p(x)dx < ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density p ˜ t ˜pt := e〈x, tu〉p(x)/R(t) is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...

Exponential deficiency of convolutions of densities∗

Iosif Pinelis (2012)

ESAIM: Probability and Statistics

If a probability density p(x) (x ∈ ℝk) is bounded and R(t) := ∫e〈x, tu〉p(x)dx < ∞ for some linear functional u and all t ∈ (0,1), then, for each t ∈ (0,1) and all large enough n, the n-fold convolution of the t-tilted density p ˜ t := e〈x, tu〉p(x)/R(t) is bounded. This is a corollary of a general, “non-i.i.d.” result, which is also shown to enjoy a certain optimality property. Such results and their corollaries stated in terms of the absolute integrability of the corresponding characteristic...

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2001)

ESAIM: Probability and Statistics

We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform φ -mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients....

Exponential inequalities and functional central limit theorems for random fields

Jérôme Dedecker (2010)

ESAIM: Probability and Statistics

We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform ϕ-mixing random fields, we require both finite fourth moments and an algebraic decay of the mixing coefficients. ...

Extremes in multivariate stationary normal sequences

Mateusz Wiśniewski (1998)

Applicationes Mathematicae

This paper deals with a weak convergence of maximum vectors built on the base of stationary and normal sequences of relatively strongly dependent random vectors. The discussion concentrates on the normality of limits and extends some results of McCormick and Mittal [4] to the multivariate case.

Fluctuation limit theorems for age-dependent critical binary branching systems

José Alfredo López-Mimbela, Antonio Murillo-Salas (2011)

ESAIM: Proceedings

We consider an age-dependent branching particle system in ℝd, where the particles are subject to α-stable migration (0 < α ≤ 2), critical binary branching, and general (non-arithmetic) lifetimes distribution. The population starts off from a Poisson random field in ℝd with Lebesgue intensity. We prove functional central limit theorems and strong laws of large numbers under two rescalings: high particle density, and a space-time rescaling...

Currently displaying 561 – 580 of 1890