The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps. In this book, the authors collect useful results derived from the construction of the Green function and its estimates. They provide a systematic discussion on key properties of elliptic integro-differential operators and their applications, including maximum principles, a priori estimates, existence, uniqueness, and regularity results for Dirichlet and ...
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The Green function has played a key role in the analytical approach that in recent years has led to important developments in the study of stochastic processes with jumps. In this book, the authors collect useful results derived from the construction of the Green function and its estimates. They provide a systematic discussion on key properties of elliptic integro-differential operators and their applications, including maximum principles, a priori estimates, existence, uniqueness, and regularity results for Dirichlet and oblique boundary value problems. They also show the existence and uniqueness of the invariant measure by means of the Green function and study ergodic stopping time and control problems.
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