Let Y be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic Markov jump process X, i.e. , . Ergodicity conditions for Y have been obtained. Here we investigate the tail property of the stationary distribution of this model. A characterization of the only two possible cases is established: light tail or polynomial tail. Our method is based on discretizations and renewal theory.
Soit Y une diffusion de Ornstein–Uhlenbeck dirigée par un processus Markovien de saut X stationnaire et ergodique : , . On connaît des conditions d'ergodicité pour Y. Ici on s'intéresse à la queue de la loi stationnaire de ce modèle. Par des méthodes de discrétisation et de renouvellement, on donne une caractérisation complète des deux seuls cas possibles : queue polynômiale ou existence de moment à tout ordre.
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Benoîte de Saporta 1; Jian-Feng Yao 1
@article{CRMATH_2004__339_9_643_0, author = {Beno{\^\i}te de Saporta and Jian-Feng Yao}, title = {Tail of a linear diffusion with {Markov} switching}, journal = {Comptes Rendus. Math\'ematique}, pages = {643--646}, publisher = {Elsevier}, volume = {339}, number = {9}, year = {2004}, doi = {10.1016/j.crma.2004.09.022}, language = {en}, }
Benoîte de Saporta; Jian-Feng Yao. Tail of a linear diffusion with Markov switching. Comptes Rendus. Mathématique, Volume 339 (2004) no. 9, pp. 643-646. doi : 10.1016/j.crma.2004.09.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.022/
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