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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.
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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