Large deviations and central limit theorems for Eyraud-Farlie-Gumbel-Morgenstern processes
Let \(\{X_n,n\geq 1\}\) be Eyraud-Gumbel-Morgenstern process and put \(S_n= \sum^n_{k=1} X_k\). Weak law of large numbers for \(S_n/n\), large deviations theorem for \(S_n/n\) and central limit theorem for \(S_n/n^{1/2}\) are stated. The large deviations theorem is proved under the assumptions only on marginal distributions of \(\{X_n, n\geq 1\}\).
scientific article; zbMATH DE number 1054100