Random processes associated with random points on a line
S. K. Srinivasan, K. S. S. Iyer (1965)
Applicationes Mathematicae
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S. K. Srinivasan, K. S. S. Iyer (1965)
Applicationes Mathematicae
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Kazimierz Urbanik (1975)
Colloquium Mathematicae
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R. Kaufman (1970)
Studia Mathematica
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Ch. Swartz, D. Myers (1971)
Studia Mathematica
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Petr Lachout (2017)
Kybernetika
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Random processes with convenient properties are often employed to model observed data, particularly, coming from economy and finance. We will focus our interest in random processes given implicitly as a solution of a functional equation. For example, random processes AR, ARMA, ARCH, GARCH are belonging in this wide class. Their common feature can be expressed by requirement that stated random process together with incoming innovations must fulfill a functional equation. Functional dependence...
Mustafa, Ghulam, Nosh, Nusrat Anjum, Rashid, Abdur (2005)
Lobachevskii Journal of Mathematics
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W. Dziubdziela (1976)
Applicationes Mathematicae
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Slobodanka Janković (1990)
Publications de l'Institut Mathématique
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G. Trybuś (1974)
Applicationes Mathematicae
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Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)
Studia Mathematica
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In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly...
Nguyen, Quy Hy, Nguyen, Ngoc Cuong (2015-12-08T12:59:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Z. Lozanov-Crvenković, Stevan Pilipović (1989)
Publications de l'Institut Mathématique
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F. den Hollander, R. S. dos Santos (2014)
Annales de l'I.H.P. Probabilités et statistiques
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We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the...
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.