Screen LibraryDegenerate diffusion operators arising in population biology /
"This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove th...
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| Literature type: | Book |
| Language: | English |
| Series: |
Annals of mathematics studies ;
no. 185 |
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| Summary: |
"This book provides the mathematical foundations for the analysis of a class of degenerate elliptic operators defined on manifolds with corners, which arise in a variety of applications such as population genetics, mathematical finance, and economics. The results discussed in this book prove the uniqueness of the solution to the Martingale problem and therefore the existence of the associated Markov process. Charles Epstein and Rafe Mazzeo use an "integral kernel method" to develop mathematical foundations for the study of such degenerate elliptic operators and the stochastic processes they |
| Carrier Form: | xiii, 306 pages ; 24 cm. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: |
9780691157122 (hardcover : alk. paper) 069115712X (hardcover : alk. paper) 9780691157153 (pbk. : alk. paper) : 0691157154 (pbk. : alk. paper) |
| Index Number: | QA329 |
| CLC: |
O211.62 Q145-32 O211.63 |
| Call Number: | O211.63/E645 |
| Contents: | Introduction. Part 1: Wright-Fisher geometry and the maximum principle. Wright-Fisher geometry ; Maximum principles and uniqueness theorems. -- Part 2: Analysis of model problems. The model solution operators ; Degenerate Hölder spaces ; Hölder estimates for the 1-dimensional model problems ; Hölder estimates for higher dimensional corner models ; Hölder estimates for Euclidean models ; Hölder estimates for general models. -- Part 3: Analysis of generalized Kimura diffusions. Existence of solutions ; The resolvent operator ; The semi-group on ℓ⁰(P). |