Limit theorems for continuous-time random walks in the double-array limit scheme

2006 ◽  
Vol 138 (1) ◽  
pp. 5348-5365 ◽  
Author(s):  
V. E. Bening ◽  
V. Yu. Korolev ◽  
V. N. Kolokoltsov
Keyword(s):  
Random Walks ◽  
Continuous Time ◽  
Limit Theorems ◽  
Double Array ◽  
Continuous Time Random Walks

Limit theorems for continuous-time random walks in the double-array limit scheme

2007 ◽  
Vol 146 (4) ◽  
pp. 5959-5976 ◽  
Author(s):  
V. E. Bening ◽  
V. Yu. Korolev ◽  
S. Koksharov ◽  
V. N. Kolokoltsov
Keyword(s):  
Random Walks ◽  
Continuous Time ◽  
Limit Theorems ◽  
Double Array ◽  
Continuous Time Random Walks

scholarly journals Limit theorems for some continuous-time random walks

2011 ◽  
Vol 43 (3) ◽  
pp. 782-813 ◽  
Author(s):  
M. Jara ◽  
T. Komorowski
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Transport ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transport Theory ◽  
Sufficient Conditions ◽  
Continuous Time Random Walks ◽  
Quantum Transport Theory

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(∙) andV(∙), 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.

scholarly journals Limit theorems for some continuous-time random walks

2011 ◽  
Vol 43 (03) ◽  
pp. 782-813 ◽  
Author(s):  
M. Jara ◽  
T. Komorowski
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Quantum Transport ◽  
Continuous Time ◽  
Limit Theorems ◽  
Transport Theory ◽  
Sufficient Conditions ◽  
Continuous Time Random Walks ◽  
Quantum Transport Theory

In this paper we consider the scaled limit of a continuous-time random walk (CTRW) based on a Markov chain {X n , 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 {X n , n ≥ 0} is a sequence of independent and identically distributed random variables.

scholarly journals Limit theorems for coupled continuous time random walks

2012 ◽  
Vol 40 (2) ◽  
pp. 890-891 ◽  
Author(s):  
Peter Kern ◽  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Random Walks ◽  
Continuous Time ◽  
Limit Theorems ◽  
Continuous Time Random Walks

Heterogeneous Memorized Continuous Time Random Walks in an External Force Fields

2014 ◽  
Vol 156 (6) ◽  
pp. 1111-1124 ◽  
Author(s):  
Jun Wang ◽  
Ji Zhou ◽  
Long-Jin Lv ◽  
Wei-Yuan Qiu ◽  
Fu-Yao Ren
Keyword(s):  
Random Walks ◽  
External Force ◽  
Continuous Time ◽  
Force Fields ◽  
Continuous Time Random Walks
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