On the Exponential Process associated with a CARMA-type Process
Resource
Stochastics,
DOI:10.1080/17442508.2012.654791
DOI:10.1080/17442508.2012.654791
Journal
Stochastics An International Journal of Probability and Stochastic Processes
Pages
743-762
Date Issued
2012-03-09
Date
2012-03-09
Author(s)
Shieh, Narn-Rueih
Matsui, M.
Abstract
Abstract We study the correlation decay and the expected maximal increments of the exponential processes determined by continuous-time autoregressive moving average (CARMA)-type processes of order (p, q). We consider two background driving processes, namely fractional Brownian motions and Lévy processes with exponential moments. The results presented in this paper are significant extensions of those very recent works on the Ornstein–Uhlenbeck-type case (p = 1, q = 0), and we develop more refined techniques to meet the general (p, q). In the concluding section, we discuss the perspective role of exponential CARMA-type processes in stochastic modelling of the burst phenomena in telecommunications and the leverage effect in financial econometrics.
SDGs
Type
journal article
File(s)![Thumbnail Image]()
Loading...
Name
index.html
Size
23.45 KB
Format
HTML
Checksum
(MD5):a23ac8d08cf83ae97eb6d7bc19dd95af