Volterra Integral Reduction for Boundary Diffusion Problems

This paper addresses a class of integral representations of the form \begin{equation} f(t,x)=g(t,x)+\int_0^t k(t,s)\, p(t-s,x,y)\, \partial_x f(s,y^+)\,ds, \qquad 0 \le t \le T, \end{equation} where $f$ is unknown, $p$ is the transition density of a diffusion process, and $g, k$ are prescribed funct