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Intertwining Certain Fractional Derivatives

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Abstract

We obtain an intertwining relation between some Riemann–Liouville operators of order α ∈ (1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric α-stable Lévy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and exponential functionals of Lévy processes is also discussed.

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Authors and Affiliations

  1. Département de Mathématiques, Université Libre de Bruxelles, Boulevard du Triomphe, 1050, Bruxelles, Belgium

    Pierre Patie

  2. Laboratoire Paul Painlevé, Cité Scientifique, Université Lille 1, 59655, Villeneuve d’Ascq Cedex, France

    Thomas Simon

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  1. Pierre Patie
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  2. Thomas Simon
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Correspondence to Pierre Patie.

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Patie, P., Simon, T. Intertwining Certain Fractional Derivatives. Potential Anal 36, 569–587 (2012). https://doi.org/10.1007/s11118-011-9241-1

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