Characterization of \(G\)-regularity for super-Brownian motion and consequences for parabolic partial differential equations. (English) Zbl 0943.60085

The authors give a characterization of the \(G\)-regularity for super-Brownian motion and the Brownian snake. This result can be viewed as a parabolic extension of Wiener test in an elliptic setting. They also give an estimate of the hitting probabilities for the support of super-Brownian motion at fixed time. Further they prove that if \(d\geq 2\), the support of super-Brownian motion is intersection-equivalent to the range of Brownian motion.


60J65 Brownian motion
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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