@article{AIHPB_2002__38_1_59_0, 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}, publisher = {Elsevier}, volume = {38}, number = {1}, year = {2002}, mrnumber = {1899230}, zbl = {1004.60078}, language = {en}, url = {http://www.numdam.org/item/AIHPB_2002__38_1_59_0/} }
TY - JOUR AU - Löcherbach, Eva TI - LAN and LAMN for systems of interacting diffusions with branching and immigration JO - Annales de l'I.H.P. Probabilités et statistiques PY - 2002 SP - 59 EP - 90 VL - 38 IS - 1 PB - Elsevier UR - http://www.numdam.org/item/AIHPB_2002__38_1_59_0/ LA - en ID - AIHPB_2002__38_1_59_0 ER -
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://www.numdam.org/item/AIHPB_2002__38_1_59_0/
[1] Regular Variation, Cambridge, Cambridge University Press, 1987. | MR | Zbl
, , ,[2] On occupation times for Markov processes, Trans. Amer. Math. Soc. 84 (1957) 444-458. | MR | Zbl
, ,[3] Asymptotic inference when the amount of information is random, in: , (Eds.), Proceedings of the Berkeley Conference in honour of J. Neyman and J. Kiefer, Vol. 2, Monterey, Wadsworth, 1985. | MR
,[4] Probabilités et Potentiel, Chapitres XII à XVI, Hermann, Paris, 1987. | MR | Zbl
, ,[5] Backward stochastic differential equations in finance, J. Math. Finance 7 (1) (1997) 1-71. | MR | Zbl
, , ,[6] Asymptotic behaviour of measure-valued critical branching processes, Proc. Amer. Math. Soc. 118 (4) (1993) 1251-1261. | MR | Zbl
,[7] Long time behaviour of critical branching particle systems and applications, in: (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] A characterization of limiting distributions of regular estimates, Z. Wahrscheinlichkeitsth. Verw. Geb. 14 (1970) 323-330. | MR | Zbl
,[9] On limits of some martingales arising in recurrent Markov chains, 1988, Unpublished note.
,[10] 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] Non-parametric estimation of the death rate in branching diffusions, Preprint No. 577, University Paris VI, 2000. | MR
, , ,[12] On invariant measure for branching diffusions, 1999, Unpublished note, see http://www.mathematik.uni-mainz.de/~hoepfner.
, ,[13] 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] Statistical Estimation. Asymptotic Theory, Springer, Berlin, 1981. | MR | Zbl
, ,[15] 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] Limit Theorems for Stochastic Processes, Springer, Berlin, 1987. | MR | Zbl
, ,[17] 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] Occupation time laws for birth and death processes, in: (Ed.), Proc. Fourth Berkeley Symp. Math. Stat. Prob. 2, Berkeley, University of California Press, 1961, pp. 249-273. | MR | Zbl
, ,[19] Asymptotics in Statistics, Springer, New York, 1990. | MR | Zbl
, ,[20] Statistics of Random Processes, Vols. 1,2, Springer, New York, 1978. | Zbl
, ,[21] Likelihood ratio processes for Markovian particle systems with killing and jumps, Preprint No. 551, University Paris VI, 1999. | MR
,[22] Local asymptotic mixed normality for semimartingale experiments, Probab. Theory Related Fields 92 (1992) 151-176. | MR | Zbl
,[23] Asymptotic behavior of some interacting particle systems; McKean-Vlasov and Boltzmann models, in: , (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] On Markov branching processes with immigration, Sankhya Ser. A 37 (1975) 129-138. | MR | Zbl
,[25] Backward SDE's and quasilinear PDE's, in: , (Eds.), Stochastic Partial Differential Equations and their Applications, LNCIS, 176, Springer, Berlin, 1990. | Zbl
, ,[26] A bivariate stable charakterization and domains of attraction, J. Multivar. Anal. 9 (1979) 206-221. | MR | Zbl
, ,[27] Mathematical Theory of Statistics, de Gruyter, Berlin, 1985. | MR | Zbl
,[28] 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] 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] Limits of spatial branching processes, Bernoulli 1 (1995) 171-189. | MR | Zbl
,[31] Life-periods of a branching process with immigration, Theor. Probab. Appl. 17 (1972) 174-183. | MR | Zbl
,