2017/09/04 by Chen, Zhen-Qing, Ren, Yan-Xia, Yang, Ting
#60F25 #FOS: Mathematics #Primary 60J68 #Probability (math.PR) #Secondary 60F15
paper · doi:10.48550/arxiv.1709.00847
The goal of this paper has two-folds. First, we establish skeleton and spine decompositions for superprocesses whose underlying processes are general symmetric Hunt processes. Second, we use these decompositions to obtain weak and strong law of large numbers for supercritical superprocesses where the spatial motion is a symmetric Hunt process on a locally compact metric space E and the branching mechanism takes the form ψβ(x,λ)=-β(x)λ+α(x)λ2+∫_(0,∞)(e-λy-1+λy)π(x,dy) with β\inBb(E), α∈ B+b(E) and π being a kernel from E to (0,∞) satisfying supx∈ E∫_(0,∞) (y\wedge y2) π(x,dy)