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Joint continuity of the solutions to a class of nonlinear SPDEs. (English) Zbl 1408.60055
Summary: For a one-dimensional superprocess in random environment, a nonlinear SPDE was derived by D. A. Dawson et al. [Ann. Inst. Henri Poincaré, Probab. Stat. 36, No. 2, 167–180 (2000; Zbl 0973.60077)] 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.
MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G57 Random measures
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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