Convolution-Type Derivatives, Hitting-Times of Subordinators and Time-Changed C0-semigroups

By Bruno Toaldo. 2013

116 citations recorded by the source corpus.

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 C0-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.

Subfields: Applied Mathematics, Modeling and Simulation, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/b6b0a3e7daf6476d1049b7601a7754b1f829976c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Mark M. Meerschaert
2. Bruno Toaldo
3. Anatoly N. Kochubei
4. Mohamed M. Khader

In Modeling and Simulation

1. Bruno Toaldo
2. Mark M. Meerschaert
3. Charles Tadjeran
4. Fawang Liu
5. Ian L Turner
6. Hans-Peter Scheffler
7. Vo Anh
8. Mohamed M. Khader

In Statistics and Probability

1. Mark M. Meerschaert
2. Bruno Toaldo

Citations in the corpus

• Relaxation patterns and semi-Markov dynamics (2015, methodology): “varying [34, Eq. (3.18)]. 12 MARK M. MEERSCHAERT AND BRUNO TOALDO 2.3. Time-changed processes. Theorem 2.1 and the discussion above suggests how the approaches of Meerschaert and Scheffler [35], Toaldo [51], and Magdziarz and Schilling [31] may be rearranged under a unifying framework, by resorting to”