Second Order Elliptic Integro-Differential Problems

PREFACE GLOSSARY OF BASIC NOTATIONS ELLIPTIC EQUATIONS Background Problems Not in Divergence Form Problems in Divergence Form Markov-Feller Processes INTEGRO-DIFFERENTIAL OPERATORS Discussion The Whole Space Bounded Domains Adjoint Operators Unbounded Functions and Commutator Relation with Jump Processes INTEGRO-DIFFERENTIAL EQUATIONS Problems Not in Divergence Form Problems in Divergence Form GREEN FUNCTION ESTIMATES Discussion Basic Properties Green Spaces Dirichlet Boundary Conditions INVARIANT DENSITY MEASURE Discussion Ergodicity Asymptotic Behavior Boundary Singularity STOPPING TIME PROBLEMS Discussion Setting of the Problem Variational Inequality Asymptotic Behavior ERGODIC CONTROL PROBLEMS Stochastic Control Hamilton-Jacobi-Bellman Equation BIBLIOGRAPHY INDEX