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Two-Parameter Lévy Processes Along Decreasing Paths

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  • Shai Covo

    (Bar Ilan University)

Abstract

Let $\{X_{t_{1},t_{2}}:t_{1},t_{2}\geq0\}$ be a two-parameter Lévy process on ℝ d . We study basic properties of the one-parameter process {X x(t),y(t):t∈T} where x and y are, respectively, nondecreasing and nonincreasing nonnegative continuous functions on the interval T. We focus on and characterize the case where the process has stationary increments.

Suggested Citation

  • Shai Covo, 2011. "Two-Parameter Lévy Processes Along Decreasing Paths," Journal of Theoretical Probability, Springer, vol. 24(1), pages 150-169, March.
    • Handle: RePEc:spr:jotpro:v:24:y:2011:i:1:d:10.1007_s10959-010-0277-8
    DOI: 10.1007/s10959-010-0277-8
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    References listed on IDEAS

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    1. Lagaize, Sandrine, 2001. "Hölder Exponent for a Two-Parameter Lévy Process," Journal of Multivariate Analysis, Elsevier, vol. 77(2), pages 270-285, May.
    2. Luis Valdivieso & Wim Schoutens & Francis Tuerlinckx, 2009. "Maximum likelihood estimation in processes of Ornstein-Uhlenbeck type," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 1-19, February.
    3. Ole E. Barndorff-Nielsen & Makoto Maejima & Ken-iti Sato, 2006. "Infinite Divisibility for Stochastic Processes and Time Change," Journal of Theoretical Probability, Springer, vol. 19(2), pages 411-446, June.
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