Generalized Translation Structures and Invariant Feller Semigroups

Herbert Heyer
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Herbert Heyer: Mathematisches Institut der Universität

A chapter in Mathematical Statistics and Probability Theory, 1987, pp 143-194 from Springer

Abstract: Abstract Generalized translation structures arise e.g. in the study of Markov processes associated with certain special functions. Such processes admit independent increments with respect to a translation depending on the defining special functions. In this article we discuss the canonical representation à la Lévy-Khintchine and the heat equation associated with a Feller semigroup which is translation invariant. How does the generalized translation operator come about? Some motivation seems to be in order.

Keywords: Canonical Representation; Infinitesimal Generator; Jacobi Operator; Translation Operator; Positive Definite Function (search for similar items in EconPapers)
Date: 1987
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-3963-9_12

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DOI: 10.1007/978-94-009-3963-9_12

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