Probability distribution of an integral quadratic functional on the trajectories of a complex-valued Ornstein-Uhlenbeck process (Q2571530)

Let \(z=(z(t))_{t\geq 0}\) be a complex-valud Ornstein-Uhlenbeck process. For a given \(T>0\), the functional \(J\) is defined by \(J:= \int_0^T| z(t)| ^2 dt.\) Let \(f=f(z,T)\) denote the density of \(J\). The aim of the present paper is to prove a concrete formula for \(f\). From this the asymptotic of \(f(z,T)\) as \(T\to\infty\) is derived.