Recurrence and transience of random difference equations in the critical case-Reference-Cited by-同舟云学术

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Recurrence and transience of random difference equations in the critical case

Published:2023-05-01 Issue:2 Volume:59 Page:
ISSN:0246-0203
Container-title:Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
language:
Short-container-title:Ann. Inst. H. Poincaré Probab. Statist.

Author:

Alsmeyer Gerold¹,Iksanov Alexander²

Affiliation:

1. Inst. Math. Stochastics, Department of Mathematics and Computer Science, University of Münster, Orléans-Ring 10, D-48149 Münster, Germany

2. Faculty of Computer Science and Cybernetics, Taras Shevchenko National University of Kyiv, 01601 Kyiv, Ukraine

Publisher

Institute of Mathematical Statistics

Subject

Statistics, Probability and Uncertainty,Statistics and Probability

Reference25 articles.

1. N. H. Bingham, C. M. Goldie and J. L. Teugels. Regular Variation. Encyclopedia of Mathematics and Its Applications 27. Cambridge University Press, Cambridge, 1989.

2. G. Alsmeyer, D. Buraczewski and A. Iksanov. Null recurrence and transience of random difference equations in the contractive case. J. Appl. Probab. 54 (2017) 1089–1110.

3. M. Babillot, P. Bougerol and L. Elie. The random difference equation ${X_{n}}={A_{n}}{X_{n-1}}+{B_{n}}$ in the critical case. Ann. Probab. 25 (1997) 478–493.

4. M. Benda. Schwach kontraktive dynamische Systeme (Weakly contractive dynamical systems). Ph.D. Thesis, Ludwig-Maximilians-Universität München, 1998.

5. J. Bertoin and R. A. Doney. Spitzer’s condition for random walks and Lévy processes. Ann. Inst. Henri Poincaré Probab. Stat. 33 (1997) 167–178.

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