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Gärtner–Ellis condition for squared asymptotically stationary Gaussian processes
Volume 2, Issue 3 (2015): PRESTO-2015, pp. 267–286
Marina Kleptsyna   Alain Le Breton   Bernard Ycart 1  

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https://doi.org/10.15559/15-VMSTA38CNF
Pub. online: 2 October 2015      Type: Research Article      Open accessOpen Access

1 This research was supported by Laboratoire d’Excellence TOUCAN (Toulouse Cancer).

Received
19 June 2015
Revised
18 September 2015
Accepted
18 September 2015
Published
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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Keywords
Gärtner–Ellis condition Gaussian process Laplace transform

MSC2010
60G14 60F10

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