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

Jakubowski, Jacek; Wiśniewolski, Maciej

doi:10.1090/tran/8169

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.

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