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Strassen Laws of Iterated Logarithm for Partially Observed Processes

Author

Listed:
  • M. A. Lifshits
  • M. Weber

    (UFR de Mathématique et Informatique)

Abstract

Let a Wiener process W be observed on some nonbounded set T⊂R + . We show that alter reasonable time- and space-rescaling the correspondent interpolated sample paths converge with probability one (in the usual sense of functional laws) to some limit set in C[0, 1]. The complete description of the limit set for arbitrary T is given. Unlike the various known functional laws, this limit set is not necessarily convex. We also supply an invariance principle which permits us to obtain the same results for partially observed processes generated by the sums of i.i.d. random variables.

Suggested Citation

  • M. A. Lifshits & M. Weber, 1997. "Strassen Laws of Iterated Logarithm for Partially Observed Processes," Journal of Theoretical Probability, Springer, vol. 10(1), pages 101-115, January.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:1:d:10.1023_a:1022694331667
    DOI: 10.1023/A:1022694331667
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    References listed on IDEAS

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    1. Shao, Q. M., 1995. "Strong Approximation Theorems for Independent Random Variables and Their Applications," Journal of Multivariate Analysis, Elsevier, vol. 52(1), pages 107-130, January.
    2. Rychlik, Z. & Zygo, J., 1992. "Strassen's invariance principle for random subsequences," Statistics & Probability Letters, Elsevier, vol. 13(3), pages 193-197, February.
    Full references (including those not matched with items on IDEAS)

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