Heat Kernel Method and its Applications

by Ivan G. Avramidi (Author)
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


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.

Number of Illustrations and Tables
17 in colour
Topics
Partial Differential Equations

More info and Hardcover at Springer

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