On rare and extreme events
Let \(0< S_1< S_2< \dots\) form a point process. Let \(X_1,X_2,\dots\) be independent and identically distributed random variables with common distribution function \(F(x)\). The authors review limit theorems available for the sum of \(X_{S_j}\), \(S_j\leq T\), \(T\to+\infty\), under a variety of assumptions on the point process \(S_j\), \(j\geq 1\), and on \(1- F(x)\) as \(x\to+\infty\). The results are then interpreted in terms of practical applications.
scientific article; zbMATH DE number 1884588
scientific article