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  2. Regning og matematisk analyse
  3. Differentialregning & ligninger

Degenerate Diffusion Operators Arising in Population Biology

Af: Charles L. Epstein, Rafe Mazzeo Engelsk Paperback

Degenerate Diffusion Operators Arising in Population Biology

Af: Charles L. Epstein, Rafe Mazzeo Engelsk Paperback
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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.

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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.

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Se mere i:
Produktdetaljer
Sprog: Engelsk
Sider: 320
ISBN-13: 9780691157153
Indbinding: Paperback
Udgave:
ISBN-10: 0691157154
Kategori: Differentialregning & ligninger
Udg. Dato: 7 apr 2013
Længde: 17mm
Bredde: 159mm
Højde: 235mm
Forlag: Princeton University Press
Oplagsdato: 7 apr 2013
Forfatter(e): Charles L. Epstein, Rafe Mazzeo
Forfatter(e) Charles L. Epstein, Rafe Mazzeo

Kategori Differentialregning & ligninger

ISBN-13 9780691157153

Sprog Engelsk

Indbinding Paperback

Sider 320

Udgave

Længde 17mm

Bredde 159mm

Højde 235mm

Udg. Dato 7 apr 2013

Oplagsdato 7 apr 2013

Forlag Princeton University Press

Kategori sammenhænge