Buch, Englisch, 240 Seiten, Format (B × H): 160 mm x 243 mm, Gewicht: 349 g
Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series
Buch, Englisch, 240 Seiten, Format (B × H): 160 mm x 243 mm, Gewicht: 349 g
Reihe: Chapman & Hall/CRC Research Notes in Mathematics Series
ISBN: 978-1-58488-200-8
Verlag: Chapman and Hall/CRC
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.
Zielgruppe
Postgraduate students and mathematicians specializing in partial differential equations and stochastic optimal control problems
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
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
