Estimation de Yule–Walker d'un CAR(p) observé à temps discret
Convergence en loi des H-variations d'un processus gaussien stationnaire sur R
Différents types de variations-produit pour une semi-martingale représentable à deux paramètres
Nous étendons les notions de processus croissants associés à un processus au cas des processus à paramètre bidimensionnel : existence et égalité de limites de sommes de carrés d’accroissements (conditionnés ou non) sur des rectangles, sur des segments parallèles, ou mixtes.
Linear diffusion with stationary switching regime
Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process . We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is gaussian on the other hand, we give...
Singularity functions for fractional processes : application to the fractional brownian sheet
Linear diffusion with stationary switching regime
Let be a Ornstein–Uhlenbeck diffusion governed by a stationary and ergodic process : ddd. We establish that under the condition with the stationary distribution of the regime process , the diffusion is ergodic. We also consider conditions for the existence of moments for the invariant law of when is a Markov jump process having a finite number of states. Using results on random difference equations on one hand and the fact that conditionally to , is Gaussian on the other hand, we...
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