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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Volterra integral equations of the first kind and applications to linear diffusions
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by Jacek Jakubowski and Maciej Wiśniewolski PDF
Trans. Amer. Math. Soc. 373 (2020), 7455-7472 Request permission

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.
References
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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 WiĹ›niewolski
  • Affiliation: Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland
  • MR Author ID: 986971
  • Email: m.wisniewolski@mimuw.edu.pl
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 7455-7472
  • MSC (2010): Primary 45D05, 60J25, 60G40
  • DOI: https://doi.org/10.1090/tran/8169
  • MathSciNet review: 4155213