We consider linear nth order stochastic differential equations on $[0,1]$, with linear boundary conditions supported by a finite subset of $[0,1]$. We study some features of the solution to these problems, and especially its conditional independence properties of Markovian type.
"Linear stochastic differential equations with functional boundary conditions." Ann. Probab. 31 (4) 2082 - 2108, October 2003. https://doi.org/10.1214/aop/1068646379