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Many statistical applications require establishing central limit theorems for sums/integrals $S_T\left(h\right)={\int }_{t\in I_T}h\left(X_t\right)\mathrm{d}t$ or for quadratic forms $Q_T\left(h\right)={\int }_{t,s\in I_T}\widehat{b}(t-s)h(X_t,X_s)\mathrm{d}s\mathrm{d}t$, where is a stationary process. A particularly important case is that of Appell polynomials ( ) = ( ), ( , ) = ( , ), since the “Appell expansion rank" determines typically the type of central limit theorem...