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Berry-Esseen bounds for functionals of independent random variables
Nicolas Privault, Grzegorz Serafin
We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to -statistics satisfyi…
Normal approximation for generalized U-statistics and weighted random graphs
Nicolas Privault, Grzegorz Serafin
We derive normal approximation bounds in the Wasserstein distance for sums of weighted U-statistics, based on a general distance bound for functionals of independent random variabl…
Feeling boundary by Brownian motion in a ball
Grzegorz Serafin
We provide short-time asymptotics with rates of convergence for the Laplace Dirichlet heat kernel in a ball. The boundary behaviour is precisely described. Presented results may be…
Normal approximation for sums of discrete -statistics - application to Kolmogorov bounds in random subgraph counting
Nicolas Privault, Grzegorz Serafin
We derive normal approximation bounds in the Kolmogorov distance for sums of discrete multiple integrals and -statistics made of independent Bernoulli random variables. Such bou…
Exit times densities of Bessel process
Grzegorz Serafin
We examine the density functions of the first exit times of the Bessel process from the intervals [0,1) and (0,1). First, we express them by means of the transition density functio…