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math.PR2015
Second and third orders asymptotic expansions for the distribution of particles in a branching random walk with a random environment in time
Zhi-Qiang Gao, Quansheng Liu
Consider a branching random walk in which the offspring distribution and the moving law both depend on an independent and identically distributed random environment indexed by the…
math.PR2015★ 1 cited
Exact convergence rates in central limit theorems for a branching random walk with a random environment in time
Zhiqiang Gao, Quansheng Liu
Chen [Ann. Appl. Probab. {\bf 11} (2001), 1242--1262] derived exact convergence rates in a central limit theorem and a local limit theorem for a supercritical branching Wiener proc…
math.PR2015
A generalization of Cramér large deviations for martingales
Xiequan Fan, Ion Grama, Quansheng Liu
In this note, we give a generalization of Cramér's large deviations for martingales, which can be regarded as a supplement of Fan, Grama and Liu (Stochastic Process. Appl., 2013).…