Extensions of diffusion processes on intervals and Feller's boundary conditions

Abstract

For a minimal diffusion process on $(a,b)$, any possible extension of it to a standard process on $[a,b]$ is characterized by the characteristic measures of excursions away from the boundary points $a$ and $b$. The generator of the extension is proved to be characterized by Feller's boundary condition.

References in corpus (1)

• Convergence of excursion point processes and its applications to functional limit theorems of Markov processes on a half-line