Random difference equations: An asymptotical result
Let \(X_i\) \((i\geq 1)\) be i.i.d. random variables with values in \([0,1]\) and density \(\alpha x^{\alpha-1}\) for some \(\alpha>0\). The authors prove that the recursively defined random variables \(U_n\) with \(U_1=X_1\) and \(U_n=X_n (1+U_{n-1})\) converge in distribution with an explicit limit distribution. Applications to pseudorandom numbers and shot noise are also discussed.
scientific article; zbMATH DE number 1915273
scientific article