We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process in terms of Brownian motion Bt ; moreover, we show that, under certain conditions on the functions f and g, the double integral process (DIP) D(t) = ∫ t β g(s) (∫ s α f (u) dBu ) ds 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.
Abundo, M., Pirozzi, E. (2018). Integrated Stationary Ornstein-Uhlenbeck Process, and Double Integral Processes. PHYSICA. A, 494, 265-275 [10.1016/j.physa.2017.12.043].
Integrated Stationary Ornstein-Uhlenbeck Process, and Double Integral Processes.
abundo mario
;
2018-01-01
Abstract
We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process in terms of Brownian motion Bt ; moreover, we show that, under certain conditions on the functions f and g, the double integral process (DIP) D(t) = ∫ t β g(s) (∫ s α f (u) dBu ) ds 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 | Dimensione | Formato | |
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