Selfsimilar Additive Processes and Stationary Ornstein–Uhlenbeck Type Processes

  • Alfonso Rocha-Arteaga
  • Ken-iti Sato
Part of the SpringerBriefs in Probability and Mathematical Statistics book series (SBPMS )


Selfsimilar processes on \(\mathbb {R}^{d}\) are those stochastic processes whose finite-dimensional distributions are such that any change of time scale has the same effect as some change of spatial scale. Under the condition of stochastic continuity and non-zero, the relation of the two scale changes is expressed by a positive number c called exponent. A Lévy process is selfsimilar if and only if it is strictly stable.


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© The Author(s), under exclusive license to Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alfonso Rocha-Arteaga
    • 1
  • Ken-iti Sato
    • 2
  1. 1.Facultad de Ciencias Físico-MatemáticasUniversidad Autónoma de SinaloaCuliacánMexico
  2. 2.Hachiman-yama 1101-5-103Tenpaku-kuJapan

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