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

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- by Jacek Jakubowski and Maciej WiĹ›niewolski PDF
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## 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