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 / Abundo, Mario; Pirozzi, Enrica. - In: PHYSICA. A. - ISSN 0378-4371. - 494:(2018), pp. 265-275. [10.1016/j.physa.2017.12.043]
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
