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Iterated processes and their applications to higher order differential equations

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Abstract

In this paper we construct models obtained by suitably combining Brownian motions and telegraphs in such a way that their transition functions satisfy higher-order parabolic or hyperbolic equations of different types.

Equations with time-varying coefficients are also derived by considering processes endowed either with drift or with suitable modifications of their structure.

Finally the distribution of the maximum of the iterated Brownian motion (along with some other properties) is presented.

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Authors and Affiliations

  1. Dipartimeno di Statistica, Probabilità e Statistiche Applicate, Università degli Studi di Roma “La Sapienza”, Piazzale Aldo Moro, 5-00185, Roma, Italy

    Enzo Orsingher

  2. Institute of Applied Mathematics, University of Bonn, 53115, Bonn, Germany

    Xuelei Zhao

  3. Institute of Mathematics, Shantou University, 515063, Shantou, P. R. China

    Xuelei Zhao

Authors
  1. Enzo Orsingher
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  2. Xuelei Zhao
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Additional information

This work is partially supported by the Natural Science Foundation of Guangdong Province, National Natural Science Foundation of China grant No. 19501026 and the Alexander von Humbodlt Foundation

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Orsingher, E., Zhao, X. Iterated processes and their applications to higher order differential equations. Acta Mathematica Sinica 15, 173–180 (1999). https://doi.org/10.1007/BF02650660

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  • DOI: https://doi.org/10.1007/BF02650660

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