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 Wn=∫e-txZn(dx)/Eξ ∫e-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ 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-degenerate.
Yuejiao WANG
,
Zaiming LIU
,
Quansheng LIU
,
Yingqiu LI
. ASYMPTOTIC PROPERTIES OF A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME[J]. Acta mathematica scientia, Series B, 2019
, 39(5)
: 1345
-1362
.
DOI: 10.1007/s10473-019-0513-y
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