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Li, Zenghu; Xiong, Jie

Continuous local time of a purely atomic immigration superprocess with dependent spatial motion. (English) Zbl 1128.60073

Stochastic Anal. Appl. 25, No. 6, 1273-1296 (2007).
Summary: A purely atomic immigration superprocess with dependent spatial motion in the space of tempered measures is constructed as the unique strong solution of a stochastic integral equation driven by Poisson processes based on the excursion law of a Feller branching diffusion, which generalizes the work of D. A. Dawson and Z. Li [Probab. Theory Relat. Fields 127, No. 1, 37–61 (2003; Zbl 1038.60082)]. As an application of the stochastic equation, it is proved that the superprocess possesses a local time which is Hölder continuous of order \(\alpha \) for every \( \alpha < 1/2\). We establish two scaling limit theorems for the immigration superprocess, from which we derive scaling limits for the corresponding local time.

Cited in 1 Document

MSC:

60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G57 Random measures
60H20 Stochastic integral equations

Keywords:

dependent spatial motion; excursion; immigration; local time; Poisson random measure; scaling limit theorem; superprocess

Citations:

Zbl 1038.60082
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\textit{Z. Li} and \textit{J. Xiong}, Stochastic Anal. Appl. 25, No. 6, 1273--1296 (2007; Zbl 1128.60073)
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References:

[1] DOI: 10.1214/aop/1176995579 · Zbl 0391.60007
[2] Dawson , D.A. 1993 .Measure-Valued Markov Processes. Lecture Notes in Mathematics, 1541 . Springer-Verlag , Berlin , pp. 1 – 260 . · Zbl 0799.60080
[3] DOI: 10.1007/s00440-003-0278-y · Zbl 1038.60082
[4] Dawson D.A., Electronic Journal of Probability 6 pp 1– (2001)
[5] DOI: 10.1023/B:JOTP.0000040293.67957.e3 · Zbl 1067.60085
[6] Dôku I., Scientiae Mathematicae Japonicae 64 pp 563– (2006)
[7] Fu Z.F., Osaka Journal of Mathematics 41 pp 727– (2004)
[8] Li Z.H., Chinese Journal of Contemporary Mathematics 25 pp 405– (2004)
[9] DOI: 10.1007/s00440-003-0313-z · Zbl 1059.60076
[10] DOI: 10.1007/s10440-005-6696-3 · Zbl 1078.60068
[11] DOI: 10.1007/BF00532802 · Zbl 0484.60062
[12] Revuz D., Continuous Martingales and Brownian Motion. (1991) · Zbl 0731.60002
[13] Shiga T., Journal of Mathematics of Kyoto University 30 pp 245– (1990)
[14] Walsh , J.B. 1986 .An Introduction to Stochastic Partial Differential Equations. Lecture Notes in Mathematics, 1180 . Springer-Verlag , Berlin , pp. 256 – 439 .
[15] DOI: 10.1007/s004400050124 · Zbl 0882.60092
[16] DOI: 10.1080/07362999808809560 · Zbl 0913.60091
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