Statistical computation of a superposition of infinitely many Ornstein–Uhlenbeck processes.

Superposition of Ornstein–Uhlenbeck processes, called supOU process, is an integration of (infinitely) many OU processes via Lévy bases. We present its Monte–Carlo method (MCM) based on the Markovian lift to efficiently handle the infinite-dimensional nature by a finite-dimensional truncation. In this method, the supOU process is discretized in time using an existing explicit scheme, while in the phase space by a quantile discretization. Numerical experiments are carried out to evaluate the performance of the MCM and to compare it with a Fourier inversion method. [ABSTRACT FROM AUTHOR]