Switched diffusion processes and systems of elliptic equations: a Dirichlet space approach
Z. Q. Chen, Zhengyang Zhao · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1994
The switched diffusion process associated with a weakly coupled system of elliptic equations is studied via a Dirichlet space approach and is applied to prove the existence theorem of the Cauchy initial problem for the system. A representation theorem for the solution of the Dirichlet boundary value problem and a generalised Skorohod decomposition for the reflecting switched diffusion process are obtained.