Abstract
For a one-dimensional superprocess in random environment, a nonlinear SPDE was derived by Dawson et al. (Ann Inst Henri Poincaré Probab Stat 36(2):167–180, 2000) for its density process. The time-space joint continuity of the density process was left as an open problem. In this paper we give an affirmative answer to this problem.
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Research of Z. Li was supported partially by NSFC (10525103 and 10721091) and CJSP, J. Xiong by NSF DMS-0906907, and X. Zhou by NSERC.
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Li, Z., Wang, H., Xiong, J. et al. Joint continuity of the solutions to a class of nonlinear SPDEs. Probab. Theory Relat. Fields 153, 441–469 (2012). https://doi.org/10.1007/s00440-011-0351-x
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DOI: https://doi.org/10.1007/s00440-011-0351-x
Keywords
- Superprocess
- Random environment
- Stochastic partial differential equation
Mathematics Subject Classification (2000)
- Primary: 60G57
- 60H15
- Secondary: 60J80