%0 Book Section %1 it1984infinite %A Itô, Kiyosi %B Stochastic AnalysisProceedings of the Taniguchi International Symposium on Stochastic Analysis %D 1984 %E Itô, Kiyosi %I Elsevier %K Brownian_motion Ornstein-Uhlenbeck SDE SPDE random_fields stochastic_processes %P 197 - 224 %R http://dx.doi.org/10.1016/S0924-6509(08)70394-5 %T Infinite Dimensional Ornstein-Uhlenbeck Processes %U http://www.sciencedirect.com/science/article/pii/S0924650908703945 %V 32 %X Publisher Summary 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.

@incollection{it1984infinite, abstract = {Publisher Summary 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. }, added-at = {2016-09-08T17:58:42.000+0200}, author = {Itô, Kiyosi}, biburl = {https://www.bibsonomy.org/bibtex/2127a10c6edf940a81d665ea67e9fb978/peter.ralph}, booktitle = {Stochastic AnalysisProceedings of the Taniguchi International Symposium on Stochastic Analysis}, doi = {http://dx.doi.org/10.1016/S0924-6509(08)70394-5}, editor = {Itô, Kiyosi}, interhash = {9a5cbcee0ca1c9da1f05c3ef5dd60964}, intrahash = {127a10c6edf940a81d665ea67e9fb978}, issn = {0924-6509}, keywords = {Brownian_motion Ornstein-Uhlenbeck SDE SPDE random_fields stochastic_processes}, pages = {197 - 224}, publisher = {Elsevier}, series = {North-Holland Mathematical Library }, timestamp = {2016-09-08T17:58:42.000+0200}, title = {Infinite Dimensional {Ornstein}-{Uhlenbeck} Processes }, url = {http://www.sciencedirect.com/science/article/pii/S0924650908703945}, volume = 32, year = 1984 }