EconPapers    
Economics at your fingertips  
 

Extremes of q-Ornstein–Uhlenbeck processes

Yizao Wang

Stochastic Processes and their Applications, 2018, vol. 128, issue 9, 2979-3005

Abstract: Two limit theorems are established on the extremes of a family of stationary Markov processes, known as q-Ornstein–Uhlenbeck processes with q∈(−1,1). Both results are crucially based on the weak convergence of the tangent process at the lower boundary of the domain of the process, a positive self-similar Markov process little investigated so far in the literature. The first result is the asymptotic excursion probability established by the double-sum method, with an explicit formula for the Pickands constant in this context. The second result is a Brown–Resnick-type limit theorem on the minimum process of i.i.d. copies of the q-Ornstein–Uhlenbeck process: with appropriate scalings in both time and magnitude, a new semi-min-stable process arises in the limit.

Keywords: Markov process; Self-similar process; Tangent process; Excursion probability; Double-sum method; Brown–Resnick process; Semi-min-stable process; q-Ornstein–Uhlenbeck process (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414917302685
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:spapps:v:128:y:2018:i:9:p:2979-3005

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().

 
Page updated 2018-11-10
Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:2979-3005