
Limit theorems for some continuous-time random walks
Jara, Milton; Komorowski, Tomasz (2011), Limit theorems for some continuous-time random walks, Advances in Applied Probability, 43, 3, p. 782-813. http://dx.doi.org/10.1239/aap/1316792670
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Type
Article accepté pour publication ou publiéDate
2011Journal name
Advances in Applied ProbabilityVolume
43Number
3Publisher
Applied Probability Trust
Pages
782-813
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Show full item recordAbstract (EN)
In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {Xn, n ≥ 0} and two observables, τ(∙) and V(∙), corresponding to the renewal times and jump sizes. Assuming that these observables belong to the domains of attraction of some stable laws, we give sufficient conditions on the chain that guarantee the existence of the scaled limits for CTRWs. An application of the results to a process that arises in quantum transport theory is provided. The results obtained in this paper generalize earlier results contained in Becker-Kern, Meerschaert and Scheffler (2004) and Meerschaert and Scheffler (2008), and the recent results of Henry and Straka (2011) and Jurlewicz, Kern, Meerschaert and Scheffler (2010), where {Xn, n ≥ 0} is a sequence of independent and identically distributed random variables.Subjects / Keywords
Continuous-time random walk; Markov chain; subordinator; jump processRelated items
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