Abstract
This paper surveys a class of Generalised Ornstein-Uhlenbeck (GOU) processes associated with Levy processes, which has been recently much analysed in view of its applications in the financial modelling area, among others. We motivate the Levy GOU by reviewing the framework already well understood for the “ordinary” (Gaussian) Ornstein-Uhlenbeck process, driven by Brownian motion; thus, defining it in terms of a stochastic differential equation (SDE), as the solution of this SDE, or as a time changed Brownian motion. Each of these approaches has an analogue for the GOU. Only the second approach, where the process is defined in terms of a stochastic integral, has been at all closely studied, and we take this as our definition of the GOU (see Eq. (12) below).
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