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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Volterra integral equations of the first kind and applications to linear diffusions


Authors: Jacek Jakubowski and Maciej Wiśniewolski
Journal: Trans. Amer. Math. Soc. 373 (2020), 7455-7472
MSC (2010): Primary 45D05, 60J25, 60G40
DOI: https://doi.org/10.1090/tran/8169
Published electronically: July 29, 2020
MathSciNet review: 4155213
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Abstract | References | Similar Articles | Additional Information

Abstract: An algebraic formula for the solution of a Volterra integral equation of the first kind is given in the topological algebra of locally integrable functions using the notions of convolution triple and $\phi$-deconvolution. Then, the formula is applied to problems from the theory of linear diffusions. In particular, the distributions of first hitting times, killed processes, and bridges are described.


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Additional Information

Jacek Jakubowski
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
MR Author ID: 93145
ORCID: 0000-0002-9621-7129
Email: jakub@mimuw.edu.pl

Maciej Wiśniewolski
Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
MR Author ID: 986971
Email: m.wisniewolski@mimuw.edu.pl

Keywords: Convolution algebra, Volterra integral equation, $\phi$-deconvolution, linear diffusion, killed diffusion, bridges
Received by editor(s): May 28, 2017
Received by editor(s) in revised form: October 11, 2018, June 6, 2019, February 10, 2020, and March 19, 2020
Published electronically: July 29, 2020
Article copyright: © Copyright 2020 American Mathematical Society