Convergence of Martingale and Moderate Deviations for a Branching Random Walk with a Random Environment in Time
نویسندگان
چکیده
منابع مشابه
Martingale ratio convergence in the branching random walk
We consider the boundary case in a one-dimensional supercritical branching random walk, and study two of the most important martingales: the additive martingale (Wn) and the derivative martingale (Dn). It is known that upon the system’s survival, Dn has a positive almost sure limit (Biggins and Kyprianou [9]), whereas Wn converges almost surely to 0 (Lyons [22]). Our main result says that after...
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Chen [Ann. Appl. Probab. 11 (2001), 1242–1262] derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener process. We extend Chen’s results to a branching random walk under weaker moment conditions. For the branching Wiener process, our results sharpen Chen’s by relaxing the second moment condition used by Chen to a moment condition...
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ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2016
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-016-0668-6