Exponential transform of quadratic functional and multiplicative ergodicity of a Gauss-Markov process

Marina Kleptsyna (1) , Alain Le Breton (2) , Bernard Ycart (2)

1 LMM - Laboratoire Manceau de Mathématiques
2 IPS - Inférence Processus Stochastiques

The Laplace transform of partial sums of the square of a non-centered Gauss-Markov process, conditioning on its starting point, is explicitly computed. The parameters of multiplicative ergodicity are deduced.

Mots clés: Multiplicative ergodicity; Laplace transform; Gauss-Markov processes

Domaines: Probabilités [math.PR]

Marina Kleptsyna, Alain Le Breton, Bernard Ycart. Exponential transform of quadratic functional and multiplicative ergodicity of a Gauss-Markov process. Statistics and Probability Letters, 2014, 87, pp.70-75. ⟨10.1016/j.spl.2013.12.023⟩. ⟨hal-00921152v2⟩