All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 23 Next

Displaying 441 – 460 of 779

Showing per page

On the asymptotic variance in the central limit theorem for particle filters

Benjamin Favetto (2012)

ESAIM: Probability and Statistics

Particle filter algorithms approximate a sequence of distributions by a sequence of empirical measures generated by a population of simulated particles. In the context of Hidden Markov Models (HMM), they provide approximations of the distribution of optimal filters associated to these models. For a given set of observations, the behaviour of particle filters, as the number of particles tends to infinity, is asymptotically Gaussian, and the asymptotic variance in the central limit theorem depends...

On the bounded laws of iterated logarithm in Banach space

Dianliang Deng (2010)

ESAIM: Probability and Statistics

In the present paper, by using the inequality due to Talagrand's isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.

On the bounded laws of iterated logarithm in Banach space

Dianliang Deng (2005)

ESAIM: Probability and Statistics

In the present paper, by using the inequality due to Talagrand’s isoperimetric method, several versions of the bounded law of iterated logarithm for a sequence of independent Banach space valued random variables are developed and the upper limits for the non-random constant are given.

On the central limit theorem for some birth and death processes

Tymoteusz Chojecki (2011)

Annales UMCS, Mathematica

Suppose that {Xn, n ≥ 0} is a stationary Markov chain and V is a certain function on a phase space of the chain, called an observable. We say that the observable satisfies the central limit theorem (CLT) if [...] [...] converge in law to a normal random variable, as N → +∞. For a stationary Markov chain with the L2 spectral gap the theorem holds for all V such that V (X0) is centered and square integrable, see Gordin [7]. The purpose of this article is to characterize a family of observables V for...

On the central limit theorem on IFS-events.

Jozefina Petrovicová, Riecan Beloslav (2005)

Mathware and Soft Computing

A probability theory on IFS-events has been constructed in [3], and axiomatically characterized in [4]. Here using a general system of axioms it is shown that any probability on IFS-events can be decomposed onto two probabilities on a Lukasiewicz tribe, hence some known results from [5], [6] can be used also for IFS-sets. As an application of the approach a variant of Central limit theorem is presented.

On the convergence of extreme distributions under power normalization

E. M. Nigm (2008)

Applicationes Mathematicae

This paper deals with the convergence in distribution of the maximum of n independent and identically distributed random variables under power normalization. We measure the difference between the actual and asymptotic distributions in terms of the double-log scale. The error committed when replacing the actual distribution of the maximum under power normalization by its asymptotic distribution is studied, assuming that the cumulative distribution function of the random variables is known. Finally,...

On the convergence of moments in the almost sure central limit theorem for stochastic approximation algorithms

Peggy Cénac (2013)

ESAIM: Probability and Statistics

We study the almost sure asymptotic behaviour of stochastic approximation algorithms for the search of zero of a real function. The quadratic strong law of large numbers is extended to the powers greater than one. In other words, the convergence of moments in the almost sure central limit theorem (ASCLT) is established. As a by-product of this convergence, one gets another proof of ASCLT for stochastic approximation algorithms. The convergence result is applied to several examples as estimation...

On the convergence of moments in the CLT for triangular arrays with an application to random polynomials

Christophe Cuny, Michel Weber (2006)

Colloquium Mathematicae

We give a proof of convergence of moments in the Central Limit Theorem (under the Lyapunov-Lindeberg condition) for triangular arrays, yielding a new estimate of the speed of convergence expressed in terms of νth moments. We also give an application to the convergence in the mean of the pth moments of certain random trigonometric polynomials built from triangular arrays of independent random variables, thereby extending some recent work of Borwein and Lockhart.

On the convergence of the ensemble Kalman filter

Jan Mandel, Loren Cobb, Jonathan D. Beezley (2011)

Applications of Mathematics

Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable random variables, the continuous mapping theorem gives convergence in probability of the ensemble members, and L p bounds on the ensemble then give L p convergence.

On the Law of Large Numbers for Nonmeasurable Identically Distributed Random Variables

Alexander R. Pruss (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Let Ω be a countable infinite product Ω ₁ ℕ of copies of the same probability space Ω₁, and let Ξₙ be the sequence of the coordinate projection functions from Ω to Ω₁. Let Ψ be a possibly nonmeasurable function from Ω₁ to ℝ, and let Xₙ(ω) = Ψ(Ξₙ(ω)). Then we can think of Xₙ as a sequence of independent but possibly nonmeasurable random variables on Ω. Let Sₙ = X₁ + ⋯ + Xₙ. By the ordinary Strong Law of Large Numbers, we almost surely have E * [ X ₁ ] ≤ l i m i n f S ₙ / n ≤ l i m s u p S ₙ / n ≤ E * [ X ₁ ] , where E * and E* are the lower and upper expectations. We ask...

On the limiting empirical measure of eigenvalues of the sum of rank one matrices with log-concave distribution

A. Pajor, L. Pastur (2009)

Studia Mathematica

We consider n × n real symmetric and hermitian random matrices Hₙ that are sums of a non-random matrix H ₙ ( 0 ) and of mₙ rank-one matrices determined by i.i.d. isotropic random vectors with log-concave probability law and real amplitudes. This is an analog of the setting of Marchenko and Pastur [Mat. Sb. 72 (1967)]. We prove that if mₙ/n → c ∈ [0,∞) as n → ∞, and the distribution of eigenvalues of H ₙ ( 0 ) and the distribution of amplitudes converge weakly, then the distribution of eigenvalues of Hₙ converges...

Currently displaying 441 – 460 of 779