Convergence of complex martingale for a branching random walk in an independent and identically distributed environment

We consider an ℝ d -valued discrete time branching random walk in an independent and identically distributed environment indexed by time n ∈ ℕ . Let W n ( z ) ( z ∈ ℂ d ) be the natural complex martingale of the process. We show necessary and sufficient conditions for the L α -convergence of W n ( z...

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Bibliographic Details
Published inFrontiers of mathematics in China Vol. 16; no. 1; pp. 187 - 209
Main Authors WANG, Xin, LIANG, Xingang, HUANG, Chunmao
Format Journal Article
LanguageEnglish
Published Beijing Higher Education Press 01.02.2021
Springer Nature B.V
Subjects
Branching random walk
complex martingale
Convergence
L α -convergenc
Martingales
Mathematics
Mathematics and Statistics
moments
random environment
Random walk
Research Article
uniform convergence
moments
convergence
Branching random walk
random environment
uniform convergence
60J80
60K37
complex martingale
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Summary:We consider an ℝ d -valued discrete time branching random walk in an independent and identically distributed environment indexed by time n ∈ ℕ . Let W n ( z ) ( z ∈ ℂ d ) be the natural complex martingale of the process. We show necessary and sufficient conditions for the L α -convergence of W n ( z ) for α >1, as well as its uniform convergence region.
Bibliography:moments
Branching random walk
random environment
uniform convergence
Document received on :2020-04-17
Document accepted on :2020-11-23
L α -convergenc
complex martingale
ISSN:1673-3452
1673-3576
DOI:10.1007/s11464-021-0882-0