Frontiers of Mathematics in China >
Domain of attraction of quasi-stationary distribution for one-dimensional diffusions
Received date: 07 Sep 2014
Accepted date: 24 Dec 2015
Published date: 18 Apr 2016
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We study quasi-stationarity for one-dimensional diffusions killed at 0, when 0 is a regular boundary and+∞ is an entrance boundary. We give a necessary and sufficient condition for the existence of exactly one quasistationary distribution, and we also show that this distribution attracts all initial distributions.
Hanjun ZHANG , Guoman HE . Domain of attraction of quasi-stationary distribution for one-dimensional diffusions[J]. Frontiers of Mathematics in China, 2016 , 11(2) : 411 -421 . DOI: 10.1007/s11464-016-0515-1
1 |
Cattiaux P, Collet P, Lambert A, Martínez S, Méléard S, San Martín J. Quasi-stationary distributions and diffusion models in population dynamics. Ann Probab, 2009, 37: 1926–1969
|
2 |
Chen M F. Explicit bounds of the first eigenvalue. Sci China Ser A, 2000, 43: 1051–1059
|
3 |
Collet P, Martínez S, San Martín J. Asymptotic laws for one-dimensional diffusions conditioned to nonabsorption. Ann Probab, 1995, 23: 1300–1314
|
4 |
Fukushima M, Oshima Y, Takeda M. Dirichlet Forms and Symmetric Markov Processes. 2nd rev and ext ed. Berlin: Walter de Gruyter, 2010
|
5 |
Karlin S, Taylor H M. A Second Course in Stochastic Processes. 2nd ed. New York: Academic Press, 1981
|
6 |
Kolb M, Steinsaltz D. Quasilimiting behavior for one-dimensional diffusions with killing. Ann Probab, 2012, 40: 162–212
|
7 |
Littin J. Uniqueness of quasistationary distributions and discrete spectra when ∞ is an entrance boundary and 0 is singular. J Appl Probab, 2012, 49: 719–730
|
8 |
Lladser M, San Martín J. Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process. J Appl Probab, 2000, 37: 511–520
|
9 |
Mandl P. Spectral theory of semi-groups connected with diffusion processes and its application. Czechoslovak Math J, 1961, 11: 558–569
|
10 |
Martínez S, Picco P, San Martín J. Domain of attraction of quasi-stationary distributions for the Brownian motion with drift. Adv in Appl Probab, 1998, 30: 385–408
|
11 |
Martínez S, San Martín J. Quasi-stationary distributions for a Brownian motion with drift and associated limit laws. J Appl Probab, 1994, 31: 911–920
|
12 |
Méléeard S, Villemonais D. Quasi-stationary distributions and population processes. Probab Surv, 2012, 9: 340–410
|
13 |
Pakes A G. Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state. Adv in Appl Probab, 1995, 27: 120–145
|
14 |
Pinsky R G. Explicit and almost explicit spectral calculations for diffusion operators. J Funct Anal, 2009, 256: 3279–3312
|
15 |
Steinsaltz D, Evans S N. Quasistationary distributions for one-dimensional diffusions with killing. Trans Amer Math Soc, 2007, 359: 1285–1324 (electronic)
|
16 |
Villemonais D. Approximation of quasi-stationary distributions for 1-dimensional killed diffusions with unbounded drifts. arXiv: 0905.3636v1, 2009
|
17 |
Zhang H J, He G M. Existence and construction of quasi-stationary distributions for one-dimensional diffusions. J Math Anal Appl, 2016, 434: 171–181
|
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