Finance
January 1984
The chapter discusses the infinite dimensional Ornstein-Uhlenbeck processes. The chapter proves the infinite dimensional version of the fact that an Ornstein-Uhlenbeck process, a centered Gaussian, Markov, stationary and mean-continuous process {Xt} satisfies the Langevin equation. An Orstein-Uhlenbeck process of linear random functionals is defined in the same way as in the 1-D case. There is a parallelism between the 1-D case and the infinite dimensional case, but an additional term, called the deterministic part is obtained. The chapter also discusses the continuous regular versions of the processes in consideration.