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Modern Stochastics and Applications pp 39–51Cite as

A Review on Time-Changed Pseudoprocesses and Related Distributions

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 90))

Abstract

Pseudoprocesses governed by higher-order heat-type equations are considered, and a probabilistic representation of their densities is presented. The composition of pseudoprocesses X n (t), t > 0, with stable processes \(T_{\frac{1} {n} }(t)\), t > 0, produces Cauchy processes which for odd values of n are asymmetric. Cauchy-type processes satisfying higher-order Laplace equations are considered and some of their properties are discussed. Pseudoprocesses on a unit-radius circle with densities obtained by wrapping up their counterparts on the line are examined. Various forms of Poisson kernels related to the composition of circular pseudoprocesses with stable processes are considered. The Fourier representation of the signed densities of circular pseudoprocesses is given and represents an extension of the classical circular Brownian motion.

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Authors and Affiliations

  1. Sapienza—Università di Roma, P.le Aldo Moro 5, 00185, Roma, Italy

    Enzo Orsingher

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  1. Enzo Orsingher
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Correspondence to Enzo Orsingher .

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Editors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    Volodymyr Korolyuk

  2. Laboratoire de Mathématiques Appliquées, Université de Technologie de Compiègne, Compiegne Cedex, France

    Nikolaos Limnios

  3. Dept. of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Yuliya Mishura

  4. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Lyudmyla Sakhno

  5. Dept.of Probability, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

    Georgiy Shevchenko

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Orsingher, E. (2014). A Review on Time-Changed Pseudoprocesses and Related Distributions. In: Korolyuk, V., Limnios, N., Mishura, Y., Sakhno, L., Shevchenko, G. (eds) Modern Stochastics and Applications. Springer Optimization and Its Applications, vol 90. Springer, Cham. https://doi.org/10.1007/978-3-319-03512-3_3

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