Infinite dimensional Ornstein-Uhlenbeck processes with unbounded diffusion - Approximation, quadratic variation, and Itô formula

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• 作者：John Karlsson and Jö ; rg-Uwe Lö ; bus
• 刊名：Mathematische Nachrichten
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：289
• 期：17-18
• 页码：2192-2222
• 全文大小：428K
• ISSN：1522-2616

文摘

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.