The first passage time density of Ornstein–Uhlenbeck process with continuous and impulsive excitations

Zi-Yi Chen and Yan-Mei Kang

Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 214-220

Abstract: The first passage time of the Ornstein–Uhlenbeck process plays a prototype role in various noise-induced escape problems. In order to calculate the first passage time density of the Ornstein–Uhlenbeck process modulated by continuous and impulsive periodic excitations using the second kind Volterra integral equation method, we adopt an approximation scheme of approaching Dirac delta function by alpha function to transform the involved discontinuous dynamical threshold into a smooth one. It is proven that the first passage time of the approximate model converges to the first passage time of the original model in probability as the approximation exponent alpha tends to infinity. For given parameters, our numerical realizations further demonstrate that good approximation effect can be achieved when the approximation exponent alpha is 10.

Keywords: First passage time; Ornstein–Uhlenbeck process; Coherent impulse excitation; Alpha function approximation; Convergence in probability (search for similar items in EconPapers)
Date: 2016
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S096007791630193X
Full text for ScienceDirect subscribers only

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:chsofr:v:91:y:2016:i:c:p:214-220

DOI: 10.1016/j.chaos.2016.05.018

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().