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Delayed and rushed motions through time change

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arxiv 1809.03818 v4 pith:2UQ5YNXL submitted 2018-09-11 math.PR math.AP

Raffaela Capitanelli , Mirko D'Ovidio This is my paper · ORCID
classification math.PRmath.AP
keywords baseprocessesrushedsubordinatorsdelayedimplyinversenecessarily
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We introduce a definition of delayed and rushed processes in terms of lifetimes of base processes and time-changed base processes. Then, we consider time changes given by subordinators and their inverse processes. Our analysis shows that, quite surprisingly, time-changing with inverse subordinators does not necessarily imply delay of the base process. Moreover, time-changing with subordinators does not necessarily imply rushed base process.

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