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A note on spider walks

Christophe Gallesco, Sebastian Müller, Serguei Popov (2011)

ESAIM: Probability and Statistics

Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.

A note on spider walks

Christophe Gallesco, Sebastian Müller, Serguei Popov (2012)

ESAIM: Probability and Statistics

Spider walks are systems of interacting particles. The particles move independently as long as their movements do not violate some given rules describing the relative position of the particles; moves that violate the rules are not realized. The goal of this paper is to study qualitative properties, as recurrence, transience, ergodicity, and positive rate of escape of these Markov processes.

A note on stochastic ordering of estimators of exponential reliability

Piotr Nowak (2011)

Applicationes Mathematicae

Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which the maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that the MLEs for those plans are also stochastically ordered. We also give some applications to the estimation of reliability.

A note on the almost sure limiting behavior of the maximun of a sequence of partial sums.

André Adler (1988)

Stochastica

The goal of this paper is to show that, in most strong laws of large numbers, the nth partial sum can be replaced with the largest of the first n sums. Moreover it is shown that the usual assumptions of independence and common distribution are unnecessary and that these results apply also to strong laws for Banach valued random elements.

A Note on the Asymptotic Behaviour of a Periodic Multitype Galton-Watson Branching Process

González, M., Martínez, R., Mota, M. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 60J80.In this work, the problem of the limiting behaviour of an irreducible Multitype Galton-Watson Branching Process with period d greater than 1 is considered. More specifically, almost sure convergence of some linear functionals depending on d consecutive generations is studied under hypothesis of non extinction. As consequence the main parameters of the model are given a convenient interpretation from a practical point of view. For a better understanding...

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