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We consider a centered Gaussian random field X = X t : t ∈ T with values in a Banach space $𝔹$ defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = convX t : t ∈ T n, where (T n) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b n)n≥1 with probability 1, (in the sense...

On the asymptotic probability for the deviations of dependent bootstrap means from the sample mean.

Ahmed, S.Ejaz, Li, Deli, Rosalsky, Andrew, Volodin, Andrei (2005)

Lobachevskii Journal of Mathematics

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 asymptotic variance in the central limit theorem for particle filters

Benjamin Favetto (2012)

ESAIM: Probability and Statistics

On the Azéma martingales

Michel Émery (1989)

Séminaire de probabilités de Strasbourg

On the Azéma-Yor stopping time

Isaac Meilijson (1983)

Séminaire de probabilités de Strasbourg

On the Barlow-Yor inequalities for local time

Burgess Davis (1987)

Séminaire de probabilités de Strasbourg

On the behavior of LIFO preemptive resume queues in heavy traffic.

Limic, Vlada (2000)

Electronic Communications in Probability [electronic only]

On the Bennett–Hoeffding inequality

Iosif Pinelis (2014)

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

The well-known Bennett–Hoeffding bound for sums of independent random variables is refined, by taking into account positive-part third moments, and at that significantly improved by using, instead of the class of all increasing exponential functions, a much larger class of generalized moment functions. The resulting bounds have certain optimality properties. The results can be extended in a standard manner to (the maximal functions of) (super)martingales. The proof of the main result relies on an...

On the best constant in the Khinchin-Kahane inequality

Rafał Latała, Krzysztof Oleszkiewicz (1994)

Studia Mathematica

We prove that if $r_{i}$ is the Rademacher system of functions then ${(ʃ ∥ \sum_{i = 1}^{n} x_{i} r_{i} (t) ∥^{2} d t)}^{1 / 2} \leq \sqrt 2 ʃ ∥ \sum_{i = 1}^{n} x_{i} r_{i} (t) ∥ d t$ for any sequence of vectors $x_{i}$ in any normed linear space F.

On the birth-and-assassination process, with an application to scotching a rumor in a network.

Bordenave, Charles (2008)

Electronic Journal of Probability [electronic only]

On the birthday problem: Some generalizations and applications.

Rathie, P.N., Zörnig, P. (2003)

International Journal of Mathematics and Mathematical Sciences

On the Borel-Cantelli Lemma and moments

S. Amghibech (2006)

Commentationes Mathematicae Universitatis Carolinae

We present some extensions of the Borel-Cantelli Lemma in terms of moments. Our result can be viewed as a new improvement to the Borel-Cantelli Lemma. Our proofs are based on the expansion of moments of some partial sums by using Stirling numbers. We also give a comment concerning the results of Petrov V.V., A generalization of the Borel-Cantelli Lemma, Statist. Probab. Lett. 67 (2004), no. 3, 233–239.

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 boundedness of Bernoulli processes over thin sets.

Latala, Rafal (2008)

Electronic Communications in Probability [electronic only]

On the Brunk-Chung type strong law of large numbers for sequences of blockwise m-dependent random variables

Le Van Thanh (2006)

ESAIM: Probability and Statistics

For a sequence of blockwise m-dependent random variables {Xn,n ≥ 1}, conditions are provided under which ${lim}_{n \to \infty} (\sum_{i = 1}^{n} X_{i}) / b_{n} = 0$ almost surely where {bn,n ≥ 1} is a sequence of positive constants. The results are new even when bn ≡ nr,r > 0. As special case, the Brunk-Chung strong law of large numbers is obtained for sequences of independent random variables. The current work also extends results of Móricz [Proc. Amer. Math. Soc.101 (1987) 709–715], and Gaposhkin [Teor. Veroyatnost. i Primenen. 39 (1994) 804–812]....

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