Heat Kernel Method and its Applications

Authors: Avramidi, Ivan G.

  • This book presents in depth asymptotic methods for solving parabolic partialdifferential 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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  • ISBN 978-3-319-26266-6
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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)


Table of contents (8 chapters)

Buy this book

eBook $99.00
price for Mexico (gross)
  • ISBN 978-3-319-26266-6
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $129.00
price for Mexico
  • ISBN 978-3-319-26265-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Heat Kernel Method and its Applications
Authors
Copyright
2015
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-26266-6
DOI
10.1007/978-3-319-26266-6
Hardcover ISBN
978-3-319-26265-9
Edition Number
1
Number of Pages
XIX, 390
Number of Illustrations and Tables
17 illustrations in colour
Topics