Infinite dimensional Ornstein-Uhlenbeck processes with unbounded diffusion: Approximation, quadratic variation, and Itô formula
2016 (English)In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, 1-31 p.Article in journal (Refereed) Epub ahead of print
The paper studies a class of Ornstein-Uhlenbeck processes on the classical Wiener space. These processes are associated with a diffusion type Dirichlet form whose corresponding diffusion operator is unbounded in the Cameron- Martin space. It is shown that the distributions of certain finite dimensional Ornstein-Uhlenbeck processes converge weakly to the distribution of such an infinite dimensional Ornstein-Uhlenbeck process. For the infinite dimensional processes, the ordinary scalar quadratic variation is calculated. Moreover, relative to the stochastic calculus via regularization, the scalar as well as the tensor quadratic variation are derived. A related Itô formula is presented.
Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2016. 1-31 p.
Infinite dimensional Ornstein-Uhlenbeck process, quadratic variation, Itô formula, weak approximation
IdentifiersURN: urn:nbn:se:liu:diva-122181DOI: 10.1002/mana.201500146OAI: oai:DiVA.org:liu-122181DiVA: diva2:862728
At the time for thesis presentation publication was in status: Manuscript2015-10-232015-10-232016-08-04Bibliographically approved