In this note, we study quasi-ergodicity for one-dimensional diffusions on , 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 , 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.
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@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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1016/j.crma.2018.07.009/
[1] A quasi-ergodic theorem for evanescent processes, Stoch. Process. Appl., Volume 84 (1999), pp. 177-186
[2] Quasi-stationary distributions and diffusion models in population dynamics, Ann. Probab., Volume 37 (2009), pp. 1926-1969
[3] On quasi-ergodic distribution for one-dimensional diffusions, Stat. Probab. Lett., Volume 110 (2016), pp. 175-180
[4] Stochastic Differential Equations and Diffusion Processes, North-Holland Mathematical Library, vol. 24, North-Holland, Amsterdam, 1989
[5] A Second Course in Stochastic Processes, Academic Press, New York, 1981
[6] 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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