We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process in terms of Brownian motion B(t) ; moreover, we show that, under certain conditions on the functions f and g, the double integral process (DIP) D(t) can be thought as the integral of a suitable Gauss–Markov process. Some theoretical and application details are given, among them we provide a simulation formula based on that representation by which sample paths, probability densities and first passage times of the ISOU process are obtained; the first-passage times of the DIP are also studied.
Integrated stationary Ornstein-Uhlenbeck process, and double integral processes
Pirozzi, Enrica
2018
Abstract
We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process in terms of Brownian motion B(t) ; moreover, we show that, under certain conditions on the functions f and g, the double integral process (DIP) D(t) can be thought as the integral of a suitable Gauss–Markov process. Some theoretical and application details are given, among them we provide a simulation formula based on that representation by which sample paths, probability densities and first passage times of the ISOU process are obtained; the first-passage times of the DIP are also studied.File in questo prodotto:
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