70 citations · 207 across the 35 of their papers we have counts for
4 papers · 2 filters
Cramér large deviation expansions for martingales under Bernstein's condition
Xiequan Fan, Ion Grama, Quansheng Liu
By using the conjugate distribution technique of Cramér, we obtain some expansions of large deviation probabilities for martingales with differences satisfying the conditional Bern…
Sharp large deviation results for sums of independent random variables
Xiequan Fan, Ion Grama, Quansheng Liu
We show sharp bounds for probabilities of large deviations for sums of independent random variables satisfying Bernstein's condition. One such bound is very close to the tail of th…
Sharp large deviation probabilities for sums of independent bounded random variables
Xiequan Fan, Ion Grama, Quansheng Liu
We obtain some optimal inequalities on tail probabilities for sums of independent bounded random variables. Our main result completes an upper bound on tail probabilities due to Ta…
Support and density of the limit -ary search trees distribution
Brigitte Chauvin, Quansheng Liu, Nicolas Pouyanne
The space requirements of an -ary search tree satisfies a well-known phase transition: when , the second order asymptotics is Gaussian. When , it is not Gaus…