Classes Lm and Ornstein–Uhlenbeck Type Processes

Abstract

Any non-zero Levy process does not have limit distribution as t →∞. But the Ornstein–Uhlenbeck process constructed from Brownian motion has a limit distribution as t →∞, which is Gaussian. Processes of Ornstein–Uhlenbeck type are analogues of the Ornstein–Uhlenbeck process with the role of Brownian motion played by general Levy processes. In this chapter we shall construct them, give the condition under which they have limit distributions, and study the connection with classes Lm.