Gärtner–Ellis condition for squared asymptotically stationary Gaussian processes
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 267–286
Pub. online: 2 October 2015
Type: Research Article
Open Access
Open Access
1
This research was supported by Laboratoire d’Excellence TOUCAN (Toulouse Cancer).
Received
19 June 2015
19 June 2015
Revised
18 September 2015
18 September 2015
Accepted
18 September 2015
18 September 2015
Published
2 October 2015
2 October 2015
Abstract
We establish the Gärtner–Ellis condition for the square of an asymptotically stationary Gaussian process. The same limit holds for the conditional distribution given any fixed initial point, which entails weak multiplicative ergodicity. The limit is shown to be the Laplace transform of a convolution of gamma distributions with Poisson compound of exponentials. A proof based on the Wiener–Hopf factorization induces a probabilistic interpretation of the limit in terms of a regression problem.
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