Authors:
This book presents in depth asymptotic methods for solving parabolic partial
differential equations at the level suitable for non-mathematicians
The focus is on the stochastic description
Although this book is intended for advanced undergraduate or beginning graduate students, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in partial differential equations, mathematical physics, differential geometry, singular perturbations and mathematical finance
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Table of contents (8 chapters)
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Front Matter
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Analysis
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Front Matter
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Geometry
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Front Matter
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Perturbations
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Front Matter
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Applications
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Front Matter
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Back Matter
About this book
The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented.
The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations.
Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.
Reviews
“The main theme of the monograph is the development of a short-time expansion for the heat kernel. … The monograph is well organized; each chapter starts with an abstract and ends with a section of notes, that can be effectively used to navigate through the contents. Thanks to an extensive presentation of background material, the book is well suited for undergraduate and graduate students, but can be of interest also for applied mathematicians and physicists.” (Paolo Musolino, zbMATH 1342.35001, 2016)
Authors and Affiliations
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Department of Mathematics, New Mexico Tech, Socorro, USA
Ivan Avramidi
Bibliographic Information
Book Title: Heat Kernel Method and its Applications
Authors: Ivan Avramidi
DOI: https://doi.org/10.1007/978-3-319-26266-6
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-26265-9Published: 04 December 2015
Softcover ISBN: 978-3-319-79920-9Published: 16 March 2019
eBook ISBN: 978-3-319-26266-6Published: 26 November 2015
Edition Number: 1
Number of Pages: XIX, 390
Number of Illustrations: 17 illustrations in colour
Topics: Partial Differential Equations