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Self-Similar Stable Processes with Stationary Increments

  • Norio Kôno
  • Makoto Maejima
Part of the Progress in Probabilty book series (PRPR, volume 25)

Abstract

Let T be (-∞, ∞), [0, ∞) or [0, 1]. A real- or complex-valued stochastic process X = (X(t)) t∈T is said to be H-self-similar (H-ss) if all finite-dimensional distributions of (X(ct)) and (c H X(t)) are the same for every c > 0 and to have stationary increments (si) if the finite-dimensional distributions of (X(t + b) - X(b)) do not depend on bT. A real-valued process X = (X(t)) t∈T is said to be symmetric α-stable (SαS), 0 < α ≤ 2, if any linear combination \( \sum\nolimits_{k = 1}^n {{a_k}} X\left( {{t_k}} \right)isS\alpha S\) is SαS.

Keywords

Sample Path Stable Process Fractional Brownian Motion Stationary Increment Symmetric Stable Process 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Norio Kôno
    • 1
    • 2
  • Makoto Maejima
    • 1
    • 2
  1. 1.Institute of Mathematics, Yoshida CollegeKyoto UniversityKyoto 606Japan
  2. 2.Department of MathematicsKeio UniversityHiyoshi, Yokohama 223Japan

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