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arXiv · 1308.1327

Convolution-type derivatives, hitting-times of subordinators and time-changed $C_0$-semigroups

Bruno Toaldo
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Abstract

In this paper we will take under consideration subordinators and their inverse processes (hitting-times). We will present in general the governing equations of such processes by means of convolution-type integro-differential operators similar to the fractional derivatives. Furthermore we will discuss the concept of time-changed $C_0$-semigroup in case the time-change is performed by means of the hitting-time of a subordinator. We will show that such time-change give rise to bounded linear operators not preserving the semigroup property and we will present their governing equations by using again integro-differential operators. Such operators are non-local and therefore we will investigate the presence of long-range dependence.

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Bruno Toaldo. 2014-07-23. Convolution-type derivatives, hitting-times of subordinators and time-changed $C_0$-semigroups. https://doi.org/10.1007/s11118-014-9426-5

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