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PREFACEGLOSSARY OF BASIC NOTATIONSELLIPTIC EQUATIONSBackgroundProblems Not in Divergence FormProblems in Divergence Form Markov-Feller Processes INTEGRO-DIFFERENTIAL OPERATORSDiscussion The Whole Space Bounded Domains Adjoint Operators Unbounded Functions and Commutator Relation with Jump Processes INTEGRO-DIFFERENTIAL EQUATIONSProblems Not in Divergence FormProblems in Divergence Form GREEN FUNCTION ESTIMATESDiscussion Basic Properties Green Spaces Dirichlet Boundary ConditionsINVARIANT DENSITY MEASUREDiscussion Ergodicity Asymptotic Behavior Boundary Singularity STOPPING TIME PROBLEMSDiscussion Setting of the Problem Variational InequalityAsymptotic Behavior ERGODIC CONTROL PROBLEMSStochastic Control Hamilton-Jacobi-Bellman EquationBIBLIOGRAPHYINDEX