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Mittag-Leffler's Function and Stochastic Linear Volterra Equations of Convolution Type 

Authors: S. Bonaccorsi a; L. Tubaro a
Affiliation:   a Department of Mathematics, University of Trento, Povo (TN), Italy
DOI: 10.1081/SAP-120017532
Publication Frequency: 6 issues per year
Published in: journal Stochastic Analysis and Applications, Volume 21, Issue 1 January 2003 , pages 61 - 78
Formats available: HTML (English) : PDF (English)
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Abstract

We consider the class of stochastic linear Volterra equations of convolution type defined by fractional integration kernels gρ(t)=lcub 1Γ(ρ) rcubtρ-1, ρ∈(0,2).

Using an explicit formula for the scalar resolvent function, we establish the basic properties of the stochastic convolution process WS. Our formulas are given in terms of the Mittag-Leffler's function  7532UM0001.gif
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