Distribution Tails for Solutions of Sde Driven By An Asymmetric Stable Lévy Process

• Autorzy: Eon Richard , Gradinaru Mihai

Identyfikatory

DOI

10.37190/0208-4147.40.2.7

• Języki publikacji: EN

Abstrakty

EN

The behaviour of the tails of the invariant distribution for stochastic differential equations driven by an asymmetric stable Lévy process is obtained. We generalize a result by Samorodnitsky and Grigoriu [8] where the stable driving noise was supposed to be symmetric.

Słowa kluczowe

EN

stochastic differential equation; asymmetric stable Lévy noise; tail behaviour; ergodic processes; stationary distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2020
• Tom: Vol. 40, Fasc. 2
• Strony: 317--330
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Eon Richard

• Université de Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France

autor

Gradinaru Mihai

• Université de Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France

Bibliografia

• [1] D. Applebaum, Lévy Processes and Stochastic Calculus, 2nd ed., Cambridge Univ. Press, 2011.
• [2] R. Eon, Asymptotique des solutions d’équations différentielles de type frottement perturbées par des bruits de Lévy stables, thèse de doctorat, Université de Rennes 1, 2016; https://tel.archivesouvertes.fr/tel-01388319v1.
• [3] R. Eon and M. Gradinaru, Gaussian asymptotics for a non-linear Langevin type equation driven by an α-stable Lévy noise, Electron. J. Probab. 20 (2015), art. 100, 19 pp.
• [4] O. Kallenberg, Foundations of Modern Probability, Springer, 2000.
• [5] A. M. Kulik, Exponential ergodicity of the solutions to SDE’s with a jump noise, Stochastic Process. Appl. 119 (2009), 602-632.
• [6] V. Petrov, Limit Theorems of Probability Theory. Sequences of Independent Random Variables, Oxford Univ. Press, 1995.
• [7] Yu. V. Prokhorov, An extremal problem in probability theory, Theory Probab. Appl. 4 (1959), 201-203.
• [8] G. Samorodnitsky and M. Grigoriu, Tails of solutions of certain nonlinear stochastic differential equations driven by heavy tailed Lévy motions, Stochastic Process. Appl. 105 (2003), 69-97.
• [9] T. Srokowski, Asymmetric Lévy flights in nonhomogeneous environments, J. Statist. Mech. Theory Experiment 2014, no. 5, art. P05024, 18 pp.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).