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 such a condition for the existence of the moment of order . Actually we recover in this case a result that Basak et al. [J. Math. Anal. Appl. 202 (1996) 604-622] have established using the theory of stochastic control of linear systems.
Mots clés : Ornstein-Uhlenbeck diffusion, Markov switching, jump process, random difference equations, ergodicity, existence of moments
@article{PS_2004__8__25_0, author = {Guyon, Xavier and Iovleff, Serge and Yao, Jian-Feng}, title = {Linear diffusion with stationary switching regime}, journal = {ESAIM: Probability and Statistics}, pages = {25--35}, publisher = {EDP-Sciences}, volume = {8}, year = {2004}, doi = {10.1051/ps:2003017}, mrnumber = {2085603}, zbl = {1033.60084}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2003017/} }
TY - JOUR AU - Guyon, Xavier AU - Iovleff, Serge AU - Yao, Jian-Feng TI - Linear diffusion with stationary switching regime JO - ESAIM: Probability and Statistics PY - 2004 SP - 25 EP - 35 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2003017/ DO - 10.1051/ps:2003017 LA - en ID - PS_2004__8__25_0 ER -
%0 Journal Article %A Guyon, Xavier %A Iovleff, Serge %A Yao, Jian-Feng %T Linear diffusion with stationary switching regime %J ESAIM: Probability and Statistics %D 2004 %P 25-35 %V 8 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2003017/ %R 10.1051/ps:2003017 %G en %F PS_2004__8__25_0
Guyon, Xavier; Iovleff, Serge; Yao, Jian-Feng. Linear diffusion with stationary switching regime. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 25-35. doi : 10.1051/ps:2003017. http://www.numdam.org/articles/10.1051/ps:2003017/
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