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Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Author: Charles L. Epstein

Publisher: Princeton University Press

Published: 2013-04-04

Total Pages: 321

ISBN-13: 1400846102

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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 define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Book Synopsis Degenerate Diffusion Operators Arising in Population Biology (AM-185) by : Charles L. Epstein

Download or read book Degenerate Diffusion Operators Arising in Population Biology (AM-185) written by Charles L. Epstein and published by Princeton University Press. This book was released on 2013-04-04 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Degenerate Diffusion Operators Arising in Population Biology (AM-185)

Author: Charles L. Epstein

Publisher:

Published: 2013

Total Pages: 321

ISBN-13: 9781400847181

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Book Synopsis Degenerate Diffusion Operators Arising in Population Biology (AM-185) by : Charles L. Epstein

Download or read book Degenerate Diffusion Operators Arising in Population Biology (AM-185) written by Charles L. Epstein and published by . This book was released on 2013 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Degenerate Diffusion Operators Arising in Population Biology

Author: Charles L. Epstein

Publisher: Princeton University Press

Published: 2013-04-07

Total Pages: 320

ISBN-13: 0691157154

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Book Synopsis Degenerate Diffusion Operators Arising in Population Biology by : Charles L. Epstein

Download or read book Degenerate Diffusion Operators Arising in Population Biology written by Charles L. Epstein and published by Princeton University Press. This book was released on 2013-04-07 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 define. The precise nature of the degeneracies of the principal symbol for these operators leads to solutions of the parabolic and elliptic problems that display novel regularity properties. Dually, the adjoint operator allows for rather dramatic singularities, such as measures supported on high codimensional strata of the boundary. Epstein and Mazzeo establish the uniqueness, existence, and sharp regularity properties for solutions to the homogeneous and inhomogeneous heat equations, as well as a complete analysis of the resolvent operator acting on Hölder spaces. They show that the semigroups defined by these operators have holomorphic extensions to the right half-plane. Epstein and Mazzeo also demonstrate precise asymptotic results for the long-time behavior of solutions to both the forward and backward Kolmogorov equations.

Information Geometry and Population Genetics

Author: Julian Hofrichter

Publisher: Springer

Published: 2017-02-23

Total Pages: 320

ISBN-13: 3319520458

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The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.

Book Synopsis Information Geometry and Population Genetics by : Julian Hofrichter

Download or read book Information Geometry and Population Genetics written by Julian Hofrichter and published by Springer. This book was released on 2017-02-23 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present monograph develops a versatile and profound mathematical perspective of the Wright--Fisher model of population genetics. This well-known and intensively studied model carries a rich and beautiful mathematical structure, which is uncovered here in a systematic manner. In addition to approaches by means of analysis, combinatorics and PDE, a geometric perspective is brought in through Amari's and Chentsov's information geometry. This concept allows us to calculate many quantities of interest systematically; likewise, the employed global perspective elucidates the stratification of the model in an unprecedented manner. Furthermore, the links to statistical mechanics and large deviation theory are explored and developed into powerful tools. Altogether, the manuscript provides a solid and broad working basis for graduate students and researchers interested in this field.

Advances in Harmonic Analysis and Partial Differential Equations

Author: Donatella Danielli

Publisher: American Mathematical Soc.

Published: 2020-04-09

Total Pages: 200

ISBN-13: 1470448963

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This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications. The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.

Book Synopsis Advances in Harmonic Analysis and Partial Differential Equations by : Donatella Danielli

Download or read book Advances in Harmonic Analysis and Partial Differential Equations written by Donatella Danielli and published by American Mathematical Soc.. This book was released on 2020-04-09 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis and Partial Differential Equations, held from April 21–22, 2018, at Northeastern University, Boston, Massachusetts. The book features a series of recent developments at the interface between harmonic analysis and partial differential equations and is aimed toward the theoretical and applied communities of researchers working in real, complex, and harmonic analysis, partial differential equations, and their applications. The topics covered belong to the general areas of the theory of function spaces, partial differential equations of elliptic, parabolic, and dissipative types, geometric optics, free boundary problems, and ergodic theory, and the emphasis is on a host of new concepts, methods, and results.

From Fourier Analysis and Number Theory to Radon Transforms and Geometry

Author: Hershel M. Farkas

Publisher: Springer Science & Business Media

Published: 2012-09-18

Total Pages: 567

ISBN-13: 1461440742

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A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Book Synopsis From Fourier Analysis and Number Theory to Radon Transforms and Geometry by : Hershel M. Farkas

Download or read book From Fourier Analysis and Number Theory to Radon Transforms and Geometry written by Hershel M. Farkas and published by Springer Science & Business Media. This book was released on 2012-09-18 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: A memorial conference for Leon Ehrenpreis was held at Temple University, November 15-16, 2010. In the spirit of Ehrenpreis’s contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis and a bit of applied mathematics. With the exception of one survey article, the papers in this volume are all new results in the various fields in which Ehrenpreis worked . There are papers in pure analysis, papers in number theory, papers in what may be called applied mathematics such as population biology and parallel refractors and papers in partial differential equations. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore.A biographical sketch of Leon Ehrenpreis by his daughter, a professional journalist, enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician.

Control of Degenerate and Singular Parabolic Equations

Author: Genni Fragnelli

Publisher: Springer Nature

Published: 2021-04-06

Total Pages: 105

ISBN-13: 303069349X

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This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.

Book Synopsis Control of Degenerate and Singular Parabolic Equations by : Genni Fragnelli

Download or read book Control of Degenerate and Singular Parabolic Equations written by Genni Fragnelli and published by Springer Nature. This book was released on 2021-04-06 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book collects some basic results on the null controllability for degenerate and singular parabolic problems. It aims to provide postgraduate students and senior researchers with a useful text, where they can find the desired statements and the related bibliography. For these reasons, the authors will not give all the detailed proofs of the given theorems, but just some of them, in order to show the underlying strategy in this area.

Fokker-Planck-Kolmogorov Equations

Author: Vladimir I. Bogachev

Publisher: American Mathematical Soc.

Published: 2015-12-17

Total Pages: 495

ISBN-13: 1470425580

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This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Book Synopsis Fokker-Planck-Kolmogorov Equations by : Vladimir I. Bogachev

Download or read book Fokker-Planck-Kolmogorov Equations written by Vladimir I. Bogachev and published by American Mathematical Soc.. This book was released on 2015-12-17 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an exposition of the principal concepts and results related to second order elliptic and parabolic equations for measures, the main examples of which are Fokker-Planck-Kolmogorov equations for stationary and transition probabilities of diffusion processes. Existence and uniqueness of solutions are studied along with existence and Sobolev regularity of their densities and upper and lower bounds for the latter. The target readership includes mathematicians and physicists whose research is related to diffusion processes as well as elliptic and parabolic equations.

Spaces of PL Manifolds and Categories of Simple Maps

Author: Friedhelm Waldhausen

Publisher:

Published: 1940

Total Pages: 196

ISBN-13:

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Book Synopsis Spaces of PL Manifolds and Categories of Simple Maps by : Friedhelm Waldhausen

Download or read book Spaces of PL Manifolds and Categories of Simple Maps written by Friedhelm Waldhausen and published by . This book was released on 1940 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Descent in Buildings

Author: Bernhard Matthias Mühlherr

Publisher: Annals of Mathematics Studies

Published: 2015

Total Pages: 0

ISBN-13: 9780691166902

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Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all hooks are again available in paperback. For a complete list of titles, please visit the Princeton University Press website: press.princeton.edu. The most recently published volumes include: Multi-parameter Singular Integrals, by Brian Street, Hangzhou Lectures on Eigenfunctions of the Laplacian, by Christopher D. Sogge, Chow Rings, Decomposition of the Diagonal, and the Topology of Families, by Claire Voisin, Spaces of PL Manifolds and Categories of Simple Maps, by Friedhelm Waldhausen, Bjorn Jahren, and John Rognes, Degenerate Diffusion Operators Arising in Population Biology, by Charles L. Epstein and Rafe Mazzeo, The Gross-Zagier Formula on Shimura Curves, by Xinyi Yuan, Shou-wu Zhang, and Wei Zhang, Mumford-Tate Groups and Domains: Their Geometry and Arithmetic, by Mark Green, Phillip A. Griffiths, and Matt Kerr, The Decomposition of Global Conformal Invariants, by Spyros Alexakis, Some Problems of Unlikely Intersections in Arithmetic and Geometry, by Umberto Zannier, Convolution and Equidistribution: Sato-Fate Theorems for Finite-Field Mellin Transforms, by Nicholas Katz.

Book Synopsis Descent in Buildings by : Bernhard Matthias Mühlherr

Download or read book Descent in Buildings written by Bernhard Matthias Mühlherr and published by Annals of Mathematics Studies. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all hooks are again available in paperback. For a complete list of titles, please visit the Princeton University Press website: press.princeton.edu. The most recently published volumes include: Multi-parameter Singular Integrals, by Brian Street, Hangzhou Lectures on Eigenfunctions of the Laplacian, by Christopher D. Sogge, Chow Rings, Decomposition of the Diagonal, and the Topology of Families, by Claire Voisin, Spaces of PL Manifolds and Categories of Simple Maps, by Friedhelm Waldhausen, Bjorn Jahren, and John Rognes, Degenerate Diffusion Operators Arising in Population Biology, by Charles L. Epstein and Rafe Mazzeo, The Gross-Zagier Formula on Shimura Curves, by Xinyi Yuan, Shou-wu Zhang, and Wei Zhang, Mumford-Tate Groups and Domains: Their Geometry and Arithmetic, by Mark Green, Phillip A. Griffiths, and Matt Kerr, The Decomposition of Global Conformal Invariants, by Spyros Alexakis, Some Problems of Unlikely Intersections in Arithmetic and Geometry, by Umberto Zannier, Convolution and Equidistribution: Sato-Fate Theorems for Finite-Field Mellin Transforms, by Nicholas Katz.