A weak limit theorem for generalized Jiřina processes
Yuqiang Li
Source: J. Appl. Probab. Volume 46, Number 2 (2009), 453-462.
Abstract
In this paper we prove that a sequence of scaled generalized Jiřina processes can converge weakly to a nonlinear diffusion process with Lévy jumps under certain conditions.
Primary Subjects: 60J80
Secondary Subjects: 60J60, 60E07
Keywords: Generalized branching processes; weak convergence; nonlinear diffusion processes
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676099
Digital Object Identifier: doi:10.1239/jap/1245676099
Mathematical Reviews number (MathSciNet):
MR2535825
References
Ethier, S. N. and Kurtz, T. G. (1986). Markov Processes. John Wiley, New York.
Mathematical Reviews (MathSciNet):
MR838085
Feller, W. (1951). Diffusion processes in genetics. In Proc. 2nd Berkeley Symp. Math. Statist. Prob., University of California Press, Berkeley, CA, pp. 227--246.
Mathematical Reviews (MathSciNet):
MR46022
Zentralblatt MATH:
0045.09302
Höpfner, R. (1985). On some classes of population-size-dependent Galton--Watson processes. J. Appl. Prob. 22, 25--36.
Mathematical Reviews (MathSciNet):
MR776885
Digital Object Identifier: doi:10.2307/3213745
JSTOR: links.jstor.org
Zentralblatt MATH:
0573.60079
Ispány, M., Pap, G. and Zuijlen, M. C. A. (2005). Fluctuation limit of branching processes with immigration and estimation of the means. Adv. Appl. Prob. 37, 523--538.
Mathematical Reviews (MathSciNet):
MR2144565
Digital Object Identifier: doi:10.1239/aap/1118858637
Project Euclid: euclid.aap/1118858637
Zentralblatt MATH:
1069.62065
Jiřina, M. (1960). Stochastic branching processes with continuous-state space. Czech. Math. J. 8, 292--313.
Mathematical Reviews (MathSciNet):
MR101554
Zentralblatt MATH:
0168.38602
Jiřina, M. (1969). On Feller's branching diffusion processes. Časopis. Pěst. Mat. 94, 84--90.
Mathematical Reviews (MathSciNet):
MR247676
Kawazu, K. and Watanabe, S. (1971). Branching processes with immigration and related limit theorems. Theory Prob. Appl. 16, 34--51.
Mathematical Reviews (MathSciNet):
MR290475
Klebaner, F. (1984). Geometric rate of growth in population-size-dependent branching processes. J. Appl. Prob. 21, 40--49.
Mathematical Reviews (MathSciNet):
MR732669
Digital Object Identifier: doi:10.2307/3213662
JSTOR: links.jstor.org
Zentralblatt MATH:
0544.60073
Li, Y. (2006). On a continuous-state population-size-dependent branching process and its extinction. J. Appl. Prob. 43, 195--207.
Mathematical Reviews (MathSciNet):
MR2225060
Digital Object Identifier: doi:10.1239/jap/1143936253
Project Euclid: euclid.jap/1143936253
Zentralblatt MATH:
1097.60067
Li, Y. (2009). Uniqueness of solutions of martingale problems with degenerate coefficients. Preprint. Available at http://www.paper.edu.cn/en/paper.php?serial_number=200901-298.
Li, Z.-H. (2000). Orenstein--Uhlenbeck type processes and branching processes with immigration. J. Appl. Prob. 37, 627--634.
Mathematical Reviews (MathSciNet):
MR1782440
Digital Object Identifier: doi:10.1239/jap/1014842823
Project Euclid: euclid.jap/1014842823
Zentralblatt MATH:
0977.60082
Li, Z. (2006). A limit theorem for discrete Galton--Watson branching processes with immigration. J. Appl. Prob. 43, 289--295.
Mathematical Reviews (MathSciNet):
MR2225068
Digital Object Identifier: doi:10.1239/jap/1143936261
Project Euclid: euclid.jap/1143936261
Zentralblatt MATH:
1098.60030
Lipow, C. (1977). Limiting diffusions for population-size-dependent branching processes. J. Appl. Prob. 14, 14--24.
Mathematical Reviews (MathSciNet):
MR428493
Digital Object Identifier: doi:10.2307/3213257
JSTOR: links.jstor.org
Zentralblatt MATH:
0388.60083
Rosenkranz, G. (1985). Diffusion approximation of controlled branching processes with random environments. Stoch. Anal. Appl. 3, 363--377.
Mathematical Reviews (MathSciNet):
MR806939
Digital Object Identifier: doi:10.1080/07362998508809068
Zentralblatt MATH:
0574.60089
Stroock, D. (1975). Diffusion processes associated Lévy generators. Z. Wahrscheinlichkeitsth. 32, 209--244.
Mathematical Reviews (MathSciNet):
MR433614
Digital Object Identifier: doi:10.1007/BF00532614
Journal of Applied Probability
