Second Order Elliptic Integro-Differential Problems

1st Edition

Maria Giovanna Garroni, Jose Luis Menaldi

Chapman and Hall/CRC
Published February 20, 2002
Reference - 240 Pages
ISBN 9781584882008 - CAT# C200X
Series: Chapman & Hall/CRC Research Notes in Mathematics Series

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Summary

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 Research Note, the authors-both regarded as leading experts in the field- collect several useful results derived from the construction of the Green function and its estimates.

The first three chapters form the foundation for the rest of the book, presenting key results and background in integro-differential operators, and integro-differential equations. After a summary of the properties relative to the Green function for second-order parabolic integro-differential operators, the authors explore important applications, paying particular attention to integro-differential problems with oblique boundary conditions. They show the existence and uniqueness of the invariant measure by means of the Green function, which then allows a detailed study of ergodic stopping time and control problems.

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