Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 5

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: central limit theorems

Sortuj według:

Ogranicz wyniki do:

Unusual limit theorems for the two tailed Pareto distribution

Adler André, Matuła Przemysław

Probability and Mathematical Statistics

2021

Vol. 41, Fasc. 2

267--281

We examine order statistics from a two-sided Pareto distribution. It turns out that the smallest two order statistics and the largest two order statistics have very unusual limits. We obtain strong and weak exact laws for the smallest and the largest order statistics. For such statistics we also study the generalized law of the iterated logarithm. For the second smallest and second largest order statistics we prove the central limit theorem even though their second moment is infinite.

Independence arising from interacting Fock spaces and related central limit theorem

Ben Ghorbal A., Crismale V.

Probability and Mathematical Statistics

2009

Vol. 29, Fasc. 2

251--269

We present the notion of projective independence, which abstracts, in an algebraic setting, the factorization rule for the vacuum expectation of creation-annihilations-preservation operators in interacting Fock spaces described in [3]. Furthermore, we give a central limit theorem based on such a notion and a Fock representation of the limit process.

On the almost sure central limit theorems in the joint version for the maxima and minima of some random variables

Dudziński M., Furmańczyk K.

Demonstratio Mathematica

2008

Vol. 41, nr 3

705-722

Let: {Xi} be a sequence of r.v.'s, and: Mn := max (X1,..., Xn), mn := min (X1,..., Xn). Our goal is to prove the almost sure central limit theorem for the properly normalized vector {Mn,mn}, provided: 1) {Xi} is an i.i.d. sequence, 2) {Xi} is a certain standardized stationary Gaussian sequence.

Almost sure central limit theorems for weakly dependent random variables

Rodzik B., Rychlik Z.

Demonstratio Mathematica

2001

Vol. 34, nr 2

375-384

We present almost sure central limit theorems for weakly dependnt random variables. The presented theorems generalize the results obtained by Peligrad and Shao (1995)

Central Limit Theorem in Hölder Spaces

Račkauskas A., Suquet C.

Probability and Mathematical Statistics

1999

Vol. 19, Fasc. 1

133--152

Stochastic processes are considered within the framework of Hölder spaces Hα0 as paths spaces. Using Ciesielski's isomorphisms between Hα0 and sequences spaces via the Faber Schauder triangular functions allows us to express our basic assumptions in terms of second differences of the processes, giving more flexibility. We obtain general conditions for the existence of a version with paths in Hα0 and the tightness of sequences of random elements in these spaces. Central limit theorems in Hα0 are established and convergence rates are given with respect to Prohorov and bounded Lipschitz metrics. As an application, we study the weak Hölder convergence of the characteristic empirical process.