an:01639382
Zbl 1056.82009
Garbaczewski, Piotr; Olkiewicz, Robert
Ornstein-Uhlenbeck-Cauchy process
EN
J. Math. Phys. 41, No. 10, 6843-6860 (2000).
00078565
2000
j
82C31 60G52 60H10 60J25
Summary: We combine earlier investigations of linear systems subject to L??vy fluctuations with recent attempts to give meaning to so-called L??vy flights in external force fields. We give a complete construction of the Ornstein-Uhlenbeck-Cauchy process as a fully computable paradigm example of Doob's stable noise-supported Ornstein-Uhlenbeck process. Despite the nonexistence of all moments, we determine local characteristics (forward drift) of the process, generators of forward and backward dynamics, and relevant (pseudodifferential) evolution equations. The induced nonstationary spatial process is proved to be Markovian and quite apart from its inherent discontinuity defines an associated velocity process in a probabilistic sense.