A Review on Time-Changed Pseudoprocesses and Related Distributions

Chapter
Part of the Springer Optimization and Its Applications book series (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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Sapienza—Università di RomaRomaItaly

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