2 problems

Let $K\in\mathbb{N}$ and let $Z_K$ be the centered, square-integrable limiting random variable characterized by … where $D,Z_K^{(0)},\ldots,Z_K^{(K)}$ are independent and each…

Let $w>0$ and let $(a_k)_{k\geqslant 1}$ define the distribution $\mathrm{UL}(w;(a_k)_{k\geqslant1})$. Let … Set $\pi_k=a_{k+1}\mathbbm{E}Z^{k+1}$ for $k\geqslant0$, and let…