### Optimal stopping of a random length sequence of maxima over a random barrier

Z. Porosiński (1988)

Applicationes Mathematicae

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Z. Porosiński (1988)

Applicationes Mathematicae

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R. Kaufman (1970)

Studia Mathematica

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I. Kopocińska, B. Kopociński (1987)

Applicationes Mathematicae

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M.V. Menshikov, Andrew R. Wade (2006)

Journal of the European Mathematical Society

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We give criteria for ergodicity, transience and null-recurrence for the random walk in random environment on ${\mathbb{Z}}^{+}=\{0,1,2,\cdots \}$, with reflection at the origin, where the random environment is subject to a vanishing perturbation. Our results complement existing criteria for random walks in random environments and for Markov chains with asymptotically zero drift, and are significantly different from the previously studied cases. Our method is based on a martingale technique—the method of Lyapunov functions. ...

G. Trybuś (1974)

Applicationes Mathematicae

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Kifer, Yuri (1998)

Documenta Mathematica

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W. Dziubdziela (1976)

Applicationes Mathematicae

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N. Zygouras (2013)

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

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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.

Mustafa, Ghulam, Nosh, Nusrat Anjum, Rashid, Abdur (2005)

Lobachevskii Journal of Mathematics

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A. Greven (1997)

Metrika

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Nguyen, Quy Hy, Nguyen, Ngoc Cuong (2015-12-08T12:59:38Z)

Acta Universitatis Lodziensis. Folia Mathematica

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Duheille-Bienvenüe, Frédérique, Guillotin-Plantard, Nadine (2003)

Electronic Communications in Probability [electronic only]

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Zachary, Stan, Foss, S.G. (2006)

Sibirskij Matematicheskij Zhurnal

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Agnieszka Jurlewicz

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Hubert Lacoin (2010)

Actes des rencontres du CIRM

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The directed polymer in random environment models the behavior of a polymer chain in a solution with impurities. It is a particular case of random walk in random environment. In $1+1$ dimensional environment is has been shown by Petermann that this random walk is superdiffusive. We show superdiffusivity properties are reinforced were there are long ranged correlation in the environment and that super diffusivity also occurs in higher dimensions.