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Classes Lm and Ornstein–Uhlenbeck Type Processes

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

Abstract

Any non-zero Lévy process does not have limit distribution as t →. But the Ornstein–Uhlenbeck process constructed from Brownian motion has a limit distribution as t →, which is Gaussian. Processes of Ornstein–Uhlenbeck type are analogues of the Ornstein–Uhlenbeck process with the role of Brownian motion played by general Lévy processes. In this chapter we shall construct them, give the condition under which they have limit distributions, and study the connection with classes Lm.

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Copyright information

© 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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