A Central Limit Theorem for Additive Random Functions

A Functional Central Limit Theorem for Integrals of Stationary Mixing Random Fields

“…Central limit theorems for Lebesgue integrals have been studied for a long time. In the 1970's first central limit theorems for integrals of the form Wn X(t) dt were shown [3,13], where (X(t)) t∈R d is a random field and the integration domains W n tend to R d in an appropriate way (see Section 3). Meschenmoser and Shashkin [15] showed a functional central limit theorem for Lebesgue measures of excursion sets of random fields, where the stochastic process is indexed by the level of the excursion set.…”

Asymptotic distribution of the empirical spatial cumulative distribution function predictor and prediction bands based on a subsampling method

“…For sums of random variables from r.f.s on the integer lattice Z d , Central Limit Theorems (CLTs) have been proved by Bolthausen (1982), Bulinskii and Zhurbenko (1976), and Guyon and Richardson (1984) under different sets of moment and mixing conditions. For r.f.s with a continuous spatial index, Ivanov and Leonenko (1989) obtains a CLT for certain weighted integrals of the field, assuming a strong-mixing condition.…”

On the asymptotics of the statistical Solutions of wave equation with variable coefficients

“…The proof is based on well-known theorems on the convergence of the additive functionals of the random processes (see e.g. [15], [16]). This theorems demands the boundedness of a(x).…”