no. 6
Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1025-1047. 
@article{AIHPB_2005__41_6_1025_0,
     author = {H\"opfner, Reinhard and L\"ocherbach, Eva},
     title = {Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1025--1047},
     publisher = {Elsevier},
     volume = {41},
     number = {6},
     year = {2005},
     doi = {10.1016/j.anihpb.2004.09.001},
     mrnumber = {2172208},
     zbl = {1080.60082},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2004.09.001/}
}
TY  - JOUR
AU  - Höpfner, Reinhard
AU  - Löcherbach, Eva
TI  - Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2005
SP  - 1025
EP  - 1047
VL  - 41
IS  - 6
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.anihpb.2004.09.001/
DO  - 10.1016/j.anihpb.2004.09.001
LA  - en
ID  - AIHPB_2005__41_6_1025_0
ER  - 
%0 Journal Article
%A Höpfner, Reinhard
%A Löcherbach, Eva
%T Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2005
%P 1025-1047
%V 41
%N 6
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.anihpb.2004.09.001/
%R 10.1016/j.anihpb.2004.09.001
%G en
%F AIHPB_2005__41_6_1025_0
Höpfner, Reinhard; Löcherbach, Eva. Remarks on ergodicity and invariant occupation measure in branching diffusions with immigration. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1025-1047. doi : 10.1016/j.anihpb.2004.09.001. http://www.numdam.org/articles/10.1016/j.anihpb.2004.09.001/

[1] R. Bass, Diffusions and Elliptic Operators, Springer, 1998. | MR | Zbl

[2] P. Cattiaux, Calcul stochastique et opérateurs dégénérés du second ordre I. Résolvantes, théorème de Hörmander et applications, Bull. Sci. Math. 114 (1990) 421-462. | MR | Zbl

[3] C. Dellacherie, P.A. Meyer, Probabilités et potentiel, Hermann, Paris, 1987, Chapitres XII à XVI. | MR

[4] R. Edwards, Functional Analysis. Theory and Applications, Holt Rinehart and Winston, 1965. | MR | Zbl

[5] R. Höpfner, E. Löcherbach, Limit Theorems for Null Recurrent Markov Processes, Mem. Amer. Math. Soc. 768 (2003). | MR | Zbl

[6] R. Höpfner, M. Hoffmann, E. Löcherbach, Non-parametric estimation of the death rate in branching diffusions, Scand. J. Statist. 29 (2002) 665-692. | MR | Zbl

[7] L. Hörmander, Hypoelliptic second-order differential equations, Acta Math. 119 (1967) 147-171. | MR | Zbl

[8] I. Ibragimov, R. Has'Minskii, Statistical Estimation, Springer, 1981. | MR

[9] N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North Holland-Kodansha, 1989. | MR | Zbl

[10] H. Kunita, Stochastic differential equations and stochastic flow of diffeomorhisms, in: Hennequin P. (Ed.), École d'été de probabilités de St. Flour XII, 1982, Lecture Notes in Math., vol. 1097, Springer, 1984, pp. 143-304. | MR | Zbl

[11] H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990. | MR | Zbl

[12] S. Kusuoka, D. Stroock, Applications of the Malliavin Calculus, part II, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 32 (1985) 1-76. | MR | Zbl

[13] L. Le Cam, G. Yang, Asymptotic in Statistics, Springer, 1990. | MR | Zbl

[14] E. Löcherbach, Likelihood ratio processes for Markovian particle systems with killing and jumps, Statist. Inference Stoch. Process. 5 (2002) 153-177. | MR | Zbl

[15] E. Löcherbach, LAN and LAMN for systems of interacting diffusions with branching and immigration, Ann. Inst. H. Poincaré Probab. Statist. 38 (2002) 59-90. | Numdam | MR | Zbl

[16] E. Löcherbach, Smoothness of the intensity measure density for interacting branching diffusions with immigrations, J. Funct. Anal. 215 (2004) 130-177. | MR | Zbl

[17] D. Revuz, Markov Chains, North-Holland, 1975. | MR | Zbl

[18] D. Williams, To begin at the beginning: …, in: Stochastic Integrals (Proc. Durham 1980), Lecture Notes in Math., vol. 851, Springer, 1981, pp. 1-55. | MR | Zbl

[19] A.M. Zubkov, Life-periods of a branching process with immigration, Theor. Probab. Appl. 17 (1972) 174-183. | MR | Zbl

Cité par Sources :