Details
| Original language | English |
|---|---|
| Pages (from-to) | 10-14 |
| Number of pages | 5 |
| Journal | Journal of Uncertain Systems |
| Volume | 10 |
| Issue number | 1 |
| Publication status | Published - Feb 2016 |
| Externally published | Yes |
Abstract
It is known that in the first approximation, many real-life stationary stochastic processes are well- described by an exponential covariance kernel C(u) = exp(-a|u|). Empirical evidence shows that in many practical situations, a good second approximation is provided by the modified exponential covari- ance kernel C(u) = exp(-a |u|) (1-r|u|). In this paper, we provide a theoretical explanation for this empirical phenomenon.
Keywords
- Exponential covariance kernel, Modified exponential covari-ance kernel, Stationary stochastic processes
ASJC Scopus subject areas
- Computer Science(all)
- Computer Vision and Pattern Recognition
- Mathematics(all)
- Control and Optimization
- Computer Science(all)
- Artificial Intelligence
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In: Journal of Uncertain Systems, Vol. 10, No. 1, 02.2016, p. 10-14.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Why Modified exponential covariance kernel is empirically successful
T2 - A theoretical explanation
AU - Kosheleva, Olga
AU - Beer, Michael
PY - 2016/2
Y1 - 2016/2
N2 - It is known that in the first approximation, many real-life stationary stochastic processes are well- described by an exponential covariance kernel C(u) = exp(-a|u|). Empirical evidence shows that in many practical situations, a good second approximation is provided by the modified exponential covari- ance kernel C(u) = exp(-a |u|) (1-r|u|). In this paper, we provide a theoretical explanation for this empirical phenomenon.
AB - It is known that in the first approximation, many real-life stationary stochastic processes are well- described by an exponential covariance kernel C(u) = exp(-a|u|). Empirical evidence shows that in many practical situations, a good second approximation is provided by the modified exponential covari- ance kernel C(u) = exp(-a |u|) (1-r|u|). In this paper, we provide a theoretical explanation for this empirical phenomenon.
KW - Exponential covariance kernel
KW - Modified exponential covari-ance kernel
KW - Stationary stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=84958979505&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:84958979505
VL - 10
SP - 10
EP - 14
JO - Journal of Uncertain Systems
JF - Journal of Uncertain Systems
SN - 1752-8909
IS - 1
ER -