Integrated stationary Ornstein–Uhlenbeck process, and double integral processes

Mario Abundo and Enrica Pirozzi

Physica A: Statistical Mechanics and its Applications, 2018, vol. 494, issue C, 265-275

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)=∫βtg(s)∫αsf(u)dBuds 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.

Keywords: Double integral process; Gauss–Markov process; Ornstein–Uhlenbeck process (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437117312803
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:494:y:2018:i:c:p:265-275

DOI: 10.1016/j.physa.2017.12.043

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().