We consider sequences of random variables of the type $S_n= n^{-1/2} \sum_{k=1}^n f(X_k)$, $n\geq 1$, where $X=(X_k)_{k\in \Z}$ is a $d$-dimensional Gaussian process and $f: \R^d \rightarrow \R$ is a measurable function. It is known that, under certain conditions on $f$ and the covariance...

Given a reference random variable, we study the solution of its Stein equation and obtain universal bounds on its first and second derivatives. We then extend the analysis of Nourdin and Peccati by bounding the Fortet–Mourier and Wasserstein distances from more general random variables such as...

The tails of the distribution of a mean zero, variance σ2 random variable Y satisfy concentration of measure inequalities of the form P(Y≥t)≤exp(−B(t)) forB(t)=t22(σ2+ct)for  t≥0,andB(t)=tc(logt−loglogt−σ2c)for  te whenever there exists a zero biased coupling of Y bounded by c,...