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Laws of iterated logarithm of multiparameter wiener processes

Author

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  • Paranjape, S. R.
  • Park, C.

Abstract

Let {} denote the N-parameter Wiener process on . For multiple sequences of certain independent random variables the authors find lower bounds for the distributions of maximum of partial sums of these random variables, and as a consequence a useful upper bound for the yet unknown function , c >= 0, is obtained where DN = [Pi]k = 1N [0, Tk]. The latter bound is used to give three different varieties of N-parameter generalization of the classical law of iterated logarithm for the standard Brownian motion process.

Suggested Citation

  • Paranjape, S. R. & Park, C., 1973. "Laws of iterated logarithm of multiparameter wiener processes," Journal of Multivariate Analysis, Elsevier, vol. 3(1), pages 132-136, March.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:1:p:132-136
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    Cited by:

    1. Bissantz, Nicolai & Holzmann, Hajo & Proksch, Katharina, 2014. "Confidence regions for images observed under the Radon transform," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 86-107.
    2. Allan Gut & Ulrich Stadtmüller, 2011. "On the LSL for Random Fields," Journal of Theoretical Probability, Springer, vol. 24(2), pages 422-449, June.
    3. Pramita Bagchi & Subhra Sankar Dhar, 2020. "A study on the least squares estimator of multivariate isotonic regression function," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(4), pages 1192-1221, December.
    4. Magda Peligrad & Allan Gut, 1999. "Almost-Sure Results for a Class of Dependent Random Variables," Journal of Theoretical Probability, Springer, vol. 12(1), pages 87-104, January.
    5. Deli Li & R. J. Tomkins, 1998. "Compact Laws of the Iterated Logarithm for B-Valued Random Variables with Two-Dimensional Indices," Journal of Theoretical Probability, Springer, vol. 11(2), pages 443-459, April.

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