Limit theorems for additive functionals of continuous time random walks

Kondratiev Y, Mishura Y, Shevchenko G (2021)
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics 151(2): 799-820.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Kondratiev, YuriUniBi; Mishura, Yuliya; Shevchenko, Georgiy
Abstract / Bemerkung
For a continuous-time random walk X = {X-t, t >= 0} (in general non-Markov), we study the asymptotic behaviour, as t -> infinity, of the normalized additive functional c(t) integral(t)(0) f(X.)ds, t >= 0. Similarly to the Markov situation, assuming that the distribution of jumps of X belongs to the domain of attraction to alpha-stable law with alpha > 1, we establish the convergence to the local time at zero of an alpha-stable Levy motion. We further study a situation where X is delayed by a random environment given by the Poisson shot-noise potential: Lambda(x,gamma) = e(-Sigma y is an element of gamma phi(x-y)), where phi: R -> [0, infinity) is a bounded function decaying sufficiently fast, and gamma is a homogeneous Poisson point process, independent of X. We find that in this case the weak limit has both 'quenched' component depending on Lambda, and a component, where Lambda is 'averaged'.
Stichworte
Continuous-time random walk; Additive functional; Domain of attraction; of stable law; alpha-stable Levy motion; Local time; Random environment; Poisson shot-noise potential
Erscheinungsjahr
2021
Zeitschriftentitel
Proceedings of the Royal Society of Edinburgh. Section A: Mathematics
Band
151
Ausgabe
2
Seite(n)
799-820
ISSN
0308-2105
eISSN
1473-7124
Page URI
https://pub.uni-bielefeld.de/record/2954688

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Kondratiev Y, Mishura Y, Shevchenko G. Limit theorems for additive functionals of continuous time random walks. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics. 2021;151(2):799-820.
Kondratiev, Y., Mishura, Y., & Shevchenko, G. (2021). Limit theorems for additive functionals of continuous time random walks. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, 151(2), 799-820. https://doi.org/10.1017/prm.2020.33
Kondratiev, Y., Mishura, Y., and Shevchenko, G. (2021). Limit theorems for additive functionals of continuous time random walks. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics 151, 799-820.
Kondratiev, Y., Mishura, Y., & Shevchenko, G., 2021. Limit theorems for additive functionals of continuous time random walks. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, 151(2), p 799-820.
Y. Kondratiev, Y. Mishura, and G. Shevchenko, “Limit theorems for additive functionals of continuous time random walks”, Proceedings of the Royal Society of Edinburgh. Section A: Mathematics, vol. 151, 2021, pp. 799-820.
Kondratiev, Y., Mishura, Y., Shevchenko, G.: Limit theorems for additive functionals of continuous time random walks. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics. 151, 799-820 (2021).
Kondratiev, Yuri, Mishura, Yuliya, and Shevchenko, Georgiy. “Limit theorems for additive functionals of continuous time random walks”. Proceedings of the Royal Society of Edinburgh. Section A: Mathematics 151.2 (2021): 799-820.

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