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Volterra integral equations of the first kind and applications to linear diffusions
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2020-07-29 , DOI: 10.1090/tran/8169 Jacek Jakubowski , Maciej Wiśniewolski
Transactions of the American Mathematical Society ( IF 1.2 ) Pub Date : 2020-07-29 , DOI: 10.1090/tran/8169 Jacek Jakubowski , Maciej Wiśniewolski
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 
-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.
中文翻译：
第一类Volterra积分方程及其在线性扩散中的应用
摘要：在局部可积函数的拓扑代数中，使用卷积三和-反卷积的概念给出了第一类Volterra积分方程解的代数公式。然后，将该公式应用于线性扩散理论中的问题。特别地，描述了首次命中时间，终止进程和桥接的分布。
更新日期：2020-10-02
-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. 中文翻译：
第一类Volterra积分方程及其在线性扩散中的应用
摘要：在局部可积函数的拓扑代数中，使用卷积三和-
反卷积的概念给出了第一类Volterra积分方程解的代数公式。然后，将该公式应用于线性扩散理论中的问题。特别地，描述了首次命中时间，终止进程和桥接的分布。
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