Abstract
We consider a discrete-time branching random walk in a stationary and ergodic environment $\xi =(\xi _{n})$ indexed by time $n\in \mathbb{N} $. Let $W_{n}(z)$ ($z\in \mathbb{C} ^{d}$) be the natural complex martingale of the process. We show sufficient conditions for its almost sure and quenched $L^{\alpha }$ convergence, as well as the existence of quenched moments and weighted moments of its limit, and also describe the exponential convergence rate.
Citation
Xiaoqiang Wang. Chunmao Huang. "Convergence of complex martingale for a branching random walk in a time random environment." Electron. Commun. Probab. 24 1 - 14, 2019. https://doi.org/10.1214/19-ECP247
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