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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