LAN and LAMN for systems of interacting diffusions with branching and immigration
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 1, pp. 59-90. 
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     author = {L\"ocherbach, Eva},
     title = {LAN and {LAMN} for systems of interacting diffusions with branching and immigration},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {59--90},
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     volume = {38},
     number = {1},
     year = {2002},
     mrnumber = {1899230},
     zbl = {1004.60078},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2002__38_1_59_0/}
}
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Löcherbach, Eva. LAN and LAMN for systems of interacting diffusions with branching and immigration. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 1, pp. 59-90. http://archive.numdam.org/item/AIHPB_2002__38_1_59_0/

[1] N.H Bingham, C.M Goldie, J.L Teugels, Regular Variation, Cambridge, Cambridge University Press, 1987. | MR | Zbl

[2] D.A Darling, M Kac, On occupation times for Markov processes, Trans. Amer. Math. Soc. 84 (1957) 444-458. | MR | Zbl

[3] R.B Davies, Asymptotic inference when the amount of information is random, in: Lecam L, Ohlsen R (Eds.), Proceedings of the Berkeley Conference in honour of J. Neyman and J. Kiefer, Vol. 2, Monterey, Wadsworth, 1985. | MR

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

[5] N El Karoui, S Peng, M.C Quenez, Backward stochastic differential equations in finance, J. Math. Finance 7 (1) (1997) 1-71. | MR | Zbl

[6] A.M Etheridge, Asymptotic behaviour of measure-valued critical branching processes, Proc. Amer. Math. Soc. 118 (4) (1993) 1251-1261. | MR | Zbl

[7] L Gorostiza, A Wakolbinger, Long time behaviour of critical branching particle systems and applications, in: Dawson D.A (Ed.), Measure Valued Processes, Stochastic Partial Differential Equations and Interacting Systems, CRM Proc. Lect. Notes, 5, AMS, Providence, 1994, pp. 119-137. | MR | Zbl

[8] J Hájek, A characterization of limiting distributions of regular estimates, Z. Wahrscheinlichkeitsth. Verw. Geb. 14 (1970) 323-330. | MR | Zbl

[9] R Höpfner, On limits of some martingales arising in recurrent Markov chains, 1988, Unpublished note.

[10] R Höpfner, On statistics of Markov step processes: representation of log-likelihood ratio processes in filtered local models, Probab. Theory Related Fields 94 (1993) 375-398. | MR | Zbl

[11] R Höpfner, M Hoffmann, E Löcherbach, Non-parametric estimation of the death rate in branching diffusions, Preprint No. 577, University Paris VI, 2000. | MR

[12] R Höpfner, E Löcherbach, On invariant measure for branching diffusions, 1999, Unpublished note, see http://www.mathematik.uni-mainz.de/~hoepfner.

[13] R Höpfner, E Löcherbach, Limit theorems for null recurrent Markov processes, Preprint 22, University of Mainz, 2000, see http://www.mathematik.uni-mainz.de/preprints/2200.html. | MR

[14] I.A Ibragimov, R.Z Khas'Minskii, Statistical Estimation. Asymptotic Theory, Springer, Berlin, 1981. | MR | Zbl

[15] N Ikeda, S Watanabe, On uniqueness and non-uniqueness of solutions for a class of non-linear equations and explosion problem for branching processes, J. Fac. Sci. Tokyo, Sect. I A 17 (1970) 187-214. | MR | Zbl

[16] J Jacod, A.N Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin, 1987. | MR | Zbl

[17] P Jeganathan, On the asymptotic theory of estimation when the limit of the log-likelihood ratio is mixed normal, Sankhya 44 (1982) 173-212. | MR | Zbl

[18] S Karlin, J Mcgregor, Occupation time laws for birth and death processes, in: Neyman J (Ed.), Proc. Fourth Berkeley Symp. Math. Stat. Prob. 2, Berkeley, University of California Press, 1961, pp. 249-273. | MR | Zbl

[19] L Lecam, G Yang, Asymptotics in Statistics, Springer, New York, 1990. | MR | Zbl

[20] R.S Liptser, A.N Shiryaev, Statistics of Random Processes, Vols. 1,2, Springer, New York, 1978. | Zbl

[21] E Löcherbach, Likelihood ratio processes for Markovian particle systems with killing and jumps, Preprint No. 551, University Paris VI, 1999. | MR

[22] H Luschgy, Local asymptotic mixed normality for semimartingale experiments, Probab. Theory Related Fields 92 (1992) 151-176. | MR | Zbl

[23] S Méléard, Asymptotic behavior of some interacting particle systems; McKean-Vlasov and Boltzmann models, in: Graham C, (Eds.), Probabilistic Models for Nonlinear Partial Differential Equations, Proc. Montecatini Terme 1995, Lecture Notes in Math., 1627, Springer, Berlin, 1996, pp. 42-95. | Zbl

[24] A.G Pakes, On Markov branching processes with immigration, Sankhya Ser. A 37 (1975) 129-138. | MR | Zbl

[25] E Pardoux, S Peng, Backward SDE's and quasilinear PDE's, in: Rozovskii B.L, Sowes R.B (Eds.), Stochastic Partial Differential Equations and their Applications, LNCIS, 176, Springer, Berlin, 1990. | Zbl

[26] S Resnick, P Greenwood, A bivariate stable charakterization and domains of attraction, J. Multivar. Anal. 9 (1979) 206-221. | MR | Zbl

[27] H Strasser, Mathematical Theory of Statistics, de Gruyter, Berlin, 1985. | MR | Zbl

[28] A.S Sznitman, Topics in Propagation of Chaos, Ecole d'été de Probabilités de Saint Flour XIX 1989, Lecture Notes in Math., 1464, Springer, New York, 1991. | MR | Zbl

[29] A Touati, Théorèmes limites pour les processus de Markov récurrents, 1988, Unpublished paper. See also C. R. Acad. Sci. Paris Série I 305 (1987) 841-844. | Zbl

[30] A Wakolbinger, Limits of spatial branching processes, Bernoulli 1 (1995) 171-189. | MR | Zbl

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