Journal ArticleDOI
Probabilistic solutions of integral equations from optimal control
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TLDR
In this article , a probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given, and this interpretation is used to obtain an approximate solution for a generalization of the integral equation.Abstract:
A probabilistic interpretation of the exact solution of a certain inhomogeneous Fredholm integral equation of the second kind is given. Then, this interpretation is used to obtain an approximate solution of a generalization of the integral equation. The approximate solutions are compared with the corresponding Neumann series solutions in various particular cases. AMS Subject Classification: Primary 45B05; Secondary 62M10, 93E20.read more
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On the First Passage Time of an Autoregressive Process over a Level and an Application to a “Disorder” Problem
Journal ArticleDOI
Martingales and first passage times of AR(1) sequences
TL;DR: In this paper, the authors used the martingale approach to find sufficient conditions for exponential boundedness of first passage times over a level for ergodic first order autoregressive sequences.
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Numerical Methods for Solving Fredholm Integral Equations of Second Kind
S. Saha Ray,P. K. Sahu +1 more
TL;DR: In this paper, the authors reviewed different numerical methods for solving both linear and nonlinear Fredholm integral equations of second kind, and discussed challenges faced by researchers in this field, and emphasized the importance of interdisciplinary effort for advancing the study on numerical method for solving integral equations.
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Improved iterative solution of linear fredholm integral equations of second kind via inverse-free iterative schemes
TL;DR: In this paper, the authors proposed an iterative scheme to approximate the non-separable kernel by using an adequate Taylor's development, and then they adapted an already known technique used for separable kernels to their case.