Infinite Variation Tempered Stable Ornstein-Uhlenbeck Processes with Discrete Observations

Reiichiro Kawai (1) , Hiroki Masuda (2)

1 Department of Mathematics [Leicester]
2 Kyushu University

We investigate transition law between consecutive observations of Ornstein-Uhlenbeck processes of infinite variation with tempered stable stationary distribution. Thanks to the Markov autoregressive structure, the transition law can be written in the exact sense as a convolution of three random components; a compound Poisson distribution and two independent tempered stable distributions, one with stability index in $(0,1)$ and the other with index in $(1,2)$.

Mots clés: Physical Sciences

Domaines: Calcul [stat.CO]

Reiichiro Kawai, Hiroki Masuda. Infinite Variation Tempered Stable Ornstein-Uhlenbeck Processes with Discrete Observations. Communications in Statistics - Simulation and Computation, 2011, 41 (01), pp.125-139. ⟨10.1080/03610918.2011.582561⟩. ⟨hal-00727116⟩