Convergence of complex martingale for a branching random walk in an independent and identically distributed environment期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Xin WANG Xingang LIANG Chunmao HUANG

Affiliation:	¹. Department of General Education, Wenzhou Business College, Wenzhou 325035, China². School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China³. Department of Mathematics, Harbin Institute of Technology (Weihai), Weihai 264209, China

Abstract:	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.

Keywords:	Branching random walk random environment moments uniform convergence complex martingale $L α$ -convergenc
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