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Lee, Kijung; Mueller, Carl; Xiong, Jie

Some properties of superprocesses under a stochastic flow. (English) Zbl 1171.60011

Ann. Inst. Henri Poincaré, Probab. Stat. 45, No. 2, 477-490 (2009).
Summary: For a superprocess under a stochastic flow in one dimension, we prove that it has a density with respect to the Lebesgue measure. A stochastic partial differential equation is derived for the density. The regularity of the solution is then proved by using Krylov’s \(L_p\)-theory for linear SPDE.

Cited in 2 Documents

MSC:

60G57 Random measures
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords:

superprocess; random environment; snake representation; stochastic partial differential equation
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\textit{K. Lee} et al., Ann. Inst. Henri Poincaré, Probab. Stat. 45, No. 2, 477--490 (2009; Zbl 1171.60011)
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