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

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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).

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Authors and Affiliations

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

    Yuhong Li

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  1. Yuhong Li
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Correspondence to Yuhong Li.

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*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.

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Li, Y. ON THE ALMOST SURELY ASYMPTOTIC BOUNDS OF A CLASS OF ORNSTEIN-UHLENBECK PROCESSES IN INFINITE DIMENSIONS*. J Syst Sci Complex 21, 416–426 (2008). https://doi.org/10.1007/s11424-008-9123-9

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  • DOI: https://doi.org/10.1007/s11424-008-9123-9

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