2 citations · 7 across the 10 of their papers we have counts for
18 papers
Fractional Burgers equation with singular initial condition
Tomasz Jakubowski, Grzegorz Serafin
We consider the fractional Burgers equation on , , with { and} and prove the existence of a s…
Laplace Dirichlet heat kernels in convex domains
Grzegorz Serafin
We provide general lower and upper bounds for Laplace Dirichlet heat kernel of convex domains. The obtained estimates precisely describe the exponential behaviou…
Backward Touchard congruence
Grzegorz Serafin
The celebrated Touchard congruence states that modulo , where is a prime number and denotes the Bell number. In this paper we study divisibility p…
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…