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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W. Szczotka, P. Żebrowski (2012)
Applicationes Mathematicae
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Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.
J. Holzheimer (1984)
Applicationes Mathematicae
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Quansheng Liu (1993)
Publications mathématiques et informatique de Rennes
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Z. Lozanov-Crvenković, Stevan Pilipović (1989)
Publications de l'Institut Mathématique
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Yakymiv, A.L. (2002)
Publications de l'Institut Mathématique. Nouvelle Série
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W. Mlak (1983)
Annales Polonici Mathematici
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Elisabeth Bauernschubert (2013)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a left-transient random walk in a random environment on that will be disturbed by cookies inducing a drift to the right of strength 1. The number of cookies per site is i.i.d. and independent of the environment. Criteria for recurrence and transience of the random walk are obtained. For this purpose we use subcritical branching processes in random environments with immigration and formulate criteria for recurrence and transience for these processes.
R. Kaufman (1970)
Studia Mathematica
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Rio Emmanuel (1997)
ESAIM: Probability and Statistics
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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...
D. Szynal (1976)
Applicationes Mathematicae
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Nguyen, Quy Hy, Nguyen, Ngoc Cuong (2015-12-08T12:59:38Z)
Acta Universitatis Lodziensis. Folia Mathematica
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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...
Ch. Swartz, D. Myers (1971)
Studia Mathematica
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Mustafa, Ghulam, Nosh, Nusrat Anjum, Rashid, Abdur (2005)
Lobachevskii Journal of Mathematics
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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...