ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS*期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS*

Authors:

Institution:

(1) College of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, 430074, China

Abstract:

Given a real-valued separable M-type 2 Banach space X with the p-th power of the norm of C ²-class, the almost sure asymptotic upper bounds of the solutions of the Ornstein-Uhlenbeck Processes described by the following equations

$\left\{ \begin{array}{ll} dz(t)=A(t, z(t))\,dt+\sigma(t, z(t))\,dW(t),\\1mm] z(0)=z_0 \in X,\end{array}\right.$

are investigated. This study generalizes the corresponding well-known finite dimensional results of Lapeyre (1989) and Mao (1992). *This research is partially supported by the National Natural Science Foundation of China under Grant No. 50579022, the Foundation of Pre-973 Program of China under Grant No. 2004CCA02500, the SRF for the ROCS, SEM, and the Talent Recruitment Foundation of HUST.

Keywords:

Almost surely asymptotic bounds infinite dimension M-type 2 Banach space Ornstein-Uhlenbeck Processes

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