no. 9
Probability theory
A note on the quasi-ergodic distribution of one-dimensional diffusions
[Une note sur la distribution quasi ergodique des diffusions en dimension 1]

Présenté par : Jean-François Le Gall

He, Guoman1
1 School of Mathematics and Statistics, Hunan University of Commerce, Changsha, Hunan 410205, PR China
Comptes Rendus. Mathématique, Tome 356 (2018) no. 9, pp. 967-972.

Nous étudions la quasi-ergodicité des diffusions unidimensionnelles sur ]0,∞[, où 0 est une frontière de sortie et ∞ une frontière d'entrée. Notre but est d'améliorer des résultats obtenus par He and Zhang (2016) [3]. Ainsi, nous retrouvons les résultats principaux de ce texte sous des hypothèses moins restrictives.

In this note, we study quasi-ergodicity for one-dimensional diffusions on (0,∞), where 0 is an exit boundary and +∞ is an entrance boundary. Our main aim is to improve some results obtained by He and Zhang (2016) [3]. In simple terms, the same main results of the above paper are obtained with more relaxed conditions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2018.07.009
He, Guoman 1

1 School of Mathematics and Statistics, Hunan University of Commerce, Changsha, Hunan 410205, PR China 
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He, Guoman. A note on the quasi-ergodic distribution of one-dimensional diffusions. Comptes Rendus. Mathématique, Tome 356 (2018) no. 9, pp. 967-972. doi : 10.1016/j.crma.2018.07.009. http://www.numdam.org/articles/10.1016/j.crma.2018.07.009/

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[2] Cattiaux, P.; Collet, P.; Lambert, A.; Martínez, S.; Méléard, S.; San Martín, J. Quasi-stationary distributions and diffusion models in population dynamics, Ann. Probab., Volume 37 (2009), pp. 1926-1969

[3] He, G.; Zhang, H. On quasi-ergodic distribution for one-dimensional diffusions, Stat. Probab. Lett., Volume 110 (2016), pp. 175-180

[4] Ikeda, N.; Watanabe, S. Stochastic Differential Equations and Diffusion Processes, North-Holland Mathematical Library, vol. 24, North-Holland, Amsterdam, 1989

[5] Karlin, S.; Taylor, H.M. A Second Course in Stochastic Processes, Academic Press, New York, 1981

[6] Littin, J. Uniqueness of quasistationary distributions and discrete spectra when ∞ is an entrance boundary and 0 is singular, J. Appl. Probab., Volume 49 (2012), pp. 719-730

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