期刊论文

Liu, Quansheng

英文

数学物理学报

1003-3998

2019

39

5

1345-1362

10.1007/s10473-019-0513-y

French government Investissements d'Avenir programFrench National Research Agency (ANR) [ANR-11-LABX-0020-01]; National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11571052, 11401590, 11731012, 11671404]; Hunan Natural Science FoundationNatural Science Foundation of Hunan Province [2017JJ2271]

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We consider a branching random walk in an independent and identically distributed random environment ξ = (ξn) indexed by the time. Let W be the limit of the martingale $$W_n=\int\;e^{-tx}Z_n(\text{d}x)/\mathbb{E}_\xi\int\;e^{-tx}Z_n(\text{d}x)$$ , with Zn denoting the counting measure of particles of generation n, and $$\mathbb{E}_\xi$$ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-de...