Second Order Elliptic Integro-Differential Problems

Maria Giovanna Garroni, Jose Luis Menaldi

218 pages, parution le 15/03/2002

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Résumé

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.

Contents

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

INV STAT: Not yet published

Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Maria Giovanna Garroni, Jose Luis Menaldi
Parution	15/03/2002
Nb. de pages	218
Format	15,5 x 23,5
Couverture	Broché
Poids	346g
Intérieur	Noir et Blanc
EAN13	9781584882008
ISBN13	978-1-58488-200-8