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Weak quenched limiting distributions for transient one-dimensional random walk in a random environment

Jonathon Peterson, Gennady Samorodnitsky (2013)

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

We consider a one-dimensional, transient random walk in a random i.i.d. environment. The asymptotic behaviour of such random walk depends to a large extent on a crucial parameter κ g t ; 0 that determines the fluctuations of the process. When 0 l t ; κ l t ; 2 , the averaged distributions of the hitting times of the random walk converge to a κ -stable distribution. However, it was shown recently that in this case there does not exist a quenched limiting distribution of the hitting times. That is, it is not true that for...

Weakly stationary processes with non–positive autocorrelations

Šárka Došlá, Jiří Anděl (2010)

Kybernetika

We deal with real weakly stationary processes { X t , t } with non-positive autocorrelations { r k } , i. e. it is assumed that r k 0 for all k = 1 , 2 , . We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies r k 0 for all k = 1 , 2 , are provided as well.

Weighting, likelihood ratio order and life distributions

Magdalena Skolimowska, Jarosław Bartoszewicz (2006)

Applicationes Mathematicae

We use weighted distributions with a weight function being a ratio of two densities to obtain some results of interest concerning life and residual life distributions. Our theorems are corollaries from results of Jain et al. (1989) and Bartoszewicz and Skolimowska (2006).

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