The growth of bi-random Dirichlet series on convergent plane (Q2744357)

Let \(F(s,\omega)= \sum^\infty_{n=1} a_nX_n(\omega)e^{-\lambda_n(\omega)s}\) and \(f(s)= \sum^\infty_{n=1} a_n e^{-E\lambda_ns}\), where \(a_n\) are complex numbers, \(\lambda_n\) and \(X_n\) are complex random variables in a probability space. The main result in this paper is that the growth order of \(F\) and \(f\) is almost surely equal under some constraints on the sequences \(a_n\), \(\lambda_n\) and \(X_n\).