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math.PR2014★ 4 cited
Martingale inequalities of type Dzhaparidze and van Zanten
Xiequan Fan, Ion Grama, Quansheng Liu
Freedman's inequality is a supermartingale counterpart to Bennett's inequality. This result shows that the tail probabilities of a supermartingale is controlled by the quadratic ch…
math.PR2014
Limit theorems for decomposable branching processes in a random environment
Vladimir Vatutin, Quansheng Liu
We study the asymptotics of the survival probability for the critical and decomposable branching processes in random environment and prove Yaglom type limit theorems for these proc…