We study the Cauchy-Dirichlet problem in half-space for linear parabolic integro-differential equations. Sufficient conditions are derived under which the problem has a unique solution in weighted Hoelder classes. The result can be used in the regularity analysis of certain functionals arising in the theory of Markov processes.
"On Cauchy-Dirichlet Problem in Half-Space for Linear Integro-Differential Equations in Weighted Hoelder Spaces." Electron. J. Probab. 10 1398 - 1416, 2005. https://doi.org/10.1214/EJP.v10-292