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Skew Brownian motion-type of extensions

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Abstract

We consider a class of possible extensions of a given symmetric Feller processZ t fromR∖{0} to the entire real lineR, depending on a parameter α∈[0, 1]. It is proved that the proposed extension exists if α=1/2; for α≠1/2, exists if and only ifZ t does not jump over 0 (e.g., ifZ t is a diffusion).

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Vuolle-Apiala, J. Skew Brownian motion-type of extensions. J Theor Probab 9, 853–861 (1996). https://doi.org/10.1007/BF02214254

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Key Words

  • Feller process
  • skew Brownian motion
  • excursion theory
  • entrance law