As main result we prove that Fejér means of Walsh–Kaczmarz–Fourier series are uniformly bounded operators from the Hardy martingale space $$\ H_{p}$$ to $$H_{p}$$ for $$ 0<p\le 1/2$$ .

We derive sharp strong convergence rates for the Euler–Maruyama scheme approximating multidimensional SDEs with multiplicative noise without imposing any regularity condition on drift coefficient. In case is additive, we show that Sobolev can be leveraged to obtain improved rate: drifts of order ??(0,1) lead rate (1+?)/2.

Abstract For an increasing sequence $$(T_n)$$ ( T n ) of one-parameter semigroups sub Markovian kernel operators over a Polish space, we study the limit semigroup and prove sufficient conditions for it to be stron...