Probability theory
A note on the quasi-ergodic distribution of one-dimensional diffusions
Comptes Rendus. Mathématique, Volume 356 (2018) no. 9, pp. 967-972.

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.

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.

Received:
Accepted:
Published online:
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
@article{CRMATH_2018__356_9_967_0,
     author = {He, Guoman},
     title = {A note on the quasi-ergodic distribution of one-dimensional diffusions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {967--972},
     publisher = {Elsevier},
     volume = {356},
     number = {9},
     year = {2018},
     doi = {10.1016/j.crma.2018.07.009},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2018.07.009/}
}
TY  - JOUR
AU  - He, Guoman
TI  - A note on the quasi-ergodic distribution of one-dimensional diffusions
JO  - Comptes Rendus. Mathématique
PY  - 2018
SP  - 967
EP  - 972
VL  - 356
IS  - 9
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2018.07.009/
DO  - 10.1016/j.crma.2018.07.009
LA  - en
ID  - CRMATH_2018__356_9_967_0
ER  - 
%0 Journal Article
%A He, Guoman
%T A note on the quasi-ergodic distribution of one-dimensional diffusions
%J Comptes Rendus. Mathématique
%D 2018
%P 967-972
%V 356
%N 9
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2018.07.009/
%R 10.1016/j.crma.2018.07.009
%G en
%F CRMATH_2018__356_9_967_0
He, Guoman. A note on the quasi-ergodic distribution of one-dimensional diffusions. Comptes Rendus. Mathématique, Volume 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/

[1] Breyer, L.A.; Roberts, G.O. A quasi-ergodic theorem for evanescent processes, Stoch. Process. Appl., Volume 84 (1999), pp. 177-186

[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

Cited by Sources: