Telegraph-Type Processes in Higher Dimensions

Nikita Ratanov and Alexander D. Kolesnik
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Nikita Ratanov: Chelyabinsk State University
Alexander D. Kolesnik: Institute of Mathematics and Computer Science

Chapter 6 in Telegraph Processes and Option Pricing, 2022, pp 297-340 from Springer

Abstract: Abstract In recent decades, finite-velocity stochastic motions in Euclidean spaces of various dimensions have been extensively studied. This chapter provides a comprehensive survey of the most important results related to the multidimensional generalisations of the one-dimensional Goldstein-Kac telegraph process. It turns out that multidimensional finite-velocity stochastic motions are described by equations which are much more complicated than the telegraph equations. These are the so-called hyperparabolic equations, whose differential operators are composed of integer powers of the telegraph and Laplace operators. We explore stochastic motions in dimensions 2, 3, 4 and 6 in detail, and present recent results in this field, including explicit distributions of the processes in low even-dimensional Euclidean spaces.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-662-65827-7_6

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DOI: 10.1007/978-3-662-65827-7_6

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