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Convolution-Type Derivatives, Hitting-Times of Subordinators and Time-Changed C 0-semigroups

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Abstract

This paper takes under consideration subordinators and their inverse processes (hitting-times). The governing equations of such processes are presented by means of convolution-type integro-differential operators similar to the fractional derivatives. Furthermore the concept of time-changed C 0-semigroup is discussed in case the time-change is performed by means of the hitting-time of a subordinator. Such time-change gives rise to bounded linear operators governed by integro-differential time-operators. Because these operators are non-local the presence of long-range dependence is investigated.

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  1. Department of Statistical Sciences, Sapienza University of Rome, Rome, Italy

    Bruno Toaldo

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Toaldo, B. Convolution-Type Derivatives, Hitting-Times of Subordinators and Time-Changed C 0-semigroups. Potential Anal 42, 115–140 (2015). https://doi.org/10.1007/s11118-014-9426-5

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