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An Almost Sure Limit Theorem for Super-Brownian Motion

Author

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  • Li Wang

    (Beijing Normal University)

Abstract

We establish an almost sure scaling limit theorem for super-Brownian motion on ℝ d associated with the semi-linear equation $u_{t}=\frac{1}{2}\Delta u+\beta u-\alpha u^{2}$ , where α and β are positive constants. In this case, the spectral theoretical assumptions required in Chen et al. (J. Funct. Anal. 254:1988–2019, 2008) are not satisfied. An example is given to show that the main results also hold for some sub-domains in ℝ d .

Suggested Citation

  • Li Wang, 2010. "An Almost Sure Limit Theorem for Super-Brownian Motion," Journal of Theoretical Probability, Springer, vol. 23(2), pages 401-416, June.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:2:d:10.1007_s10959-008-0200-8
    DOI: 10.1007/s10959-008-0200-8
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    Cited by:

    1. Li Wang, 2018. "Central Limit Theorems for Supercritical Superprocesses with Immigration," Journal of Theoretical Probability, Springer, vol. 31(2), pages 984-1012, June.
    2. Liu, Rongli & Ren, Yan-Xia & Song, Renming, 2022. "Convergence rate for a class of supercritical superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 286-327.

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