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On infinite series of independent Ornstein-Uhlenbeck processes

Author

Listed:
  • Csáki, E.
  • Csörgo, M.
  • Lin, Z. Y.
  • Révész, P.

Abstract

We establish moduli of continuity and large increment properties for stationary increment Gaussian processes in order to study the path behavior of infinite series of independent Ornstein-Uhlenbeck processes. The existence and continuity of the latter infinite series type Gaussian processes are proved via showing that under a global condition their partial sum processes converge uniformly over finite intervals with probability one.

Suggested Citation

  • Csáki, E. & Csörgo, M. & Lin, Z. Y. & Révész, P., 1991. "On infinite series of independent Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 39(1), pages 25-44, October.
    • Handle: RePEc:eee:spapps:v:39:y:1991:i:1:p:25-44
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    Cited by:

    1. Lin, Zhengyan & Hwang, Kyo-Shin & Lee, Sungchul & Choi, Yong-Kab, 2004. "Path properties of a d-dimensional Gaussian process," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 383-393, July.
    2. Lin, Z. Y., 1995. "On large increments of infinite series of Ornstein-Uhlenbeck processes," Stochastic Processes and their Applications, Elsevier, vol. 60(1), pages 161-169, November.
    3. Yong-Kab Choi, 2004. "Path properties of (N;d)-Gaussian random fields," RePAd Working Paper Series lrsp-TRS393, Département des sciences administratives, UQO.
    4. Zhang, Li-Xin, 1997. "On the fractal nature of increments of lp-valued Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 91-110, October.

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