Ornstein-Uhlenbeck-Cauchy process

We combine earlier investigations of linear systems subject to Levy fluctua tions with recent attempts to give meaning to so-called Levy flights in ext ernal force fields. We give a complete construction of the Ornstein-Uhlenbe ck-Cauchy process as a fully computable paradigm example of Doob's stable n oise-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 (pseudodifferent ial) evolution equations. The induced nonstationary spatial process is prov ed to be Markovian and quite apart from its inherent discontinuity defines an associated velocity process in a probabilistic sense. (C) 2000 American Institute of Physics. [S0022-2488(00)02410-5].