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A note on quenched moderate deviations for Sinai’s random walk in random environment

Francis Comets, Serguei Popov (2004)

ESAIM: Probability and Statistics

We consider the continuous time, one-dimensional random walk in random environment in Sinai’s regime. We show that the probability for the particle to be, at time t and in a typical environment, at a distance larger than t a ( 0 < a < 1 ) from its initial position, is exp { - Const · t a / [ ( 1 - a ) ln t ] ( 1 + o ( 1 ) ) } .

A note on quenched moderate deviations for Sinai's random walk in random environment

Francis Comets, Serguei Popov (2010)

ESAIM: Probability and Statistics

We consider the continuous time, one-dimensional random walk in random environment in Sinai's regime. We show that the probability for the particle to be, at time t and in a typical environment, at a distance larger than ta (0<a<1) from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.

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.

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