Heat Kernel Method and its Applications

Heat Kernel Method and its Applications

by Ivan Avramidi

Hardcover(1st ed. 2015)

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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, shastic 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.

Product Details

ISBN-13: 9783319262659
Publisher: Springer International Publishing
Publication date: 11/28/2015
Edition description: 1st ed. 2015
Pages: 390
Product dimensions: 6.10(w) x 9.25(h) x (d)

Table of Contents

Part I Analysis.- 1 Background in Analysis.- 2 Introduction to Partial Differential Equations.- Part II Geometry.- 3 Introduction to Differential Geometry.- Part III Perturbations.- 4 Singular Perturbations.- 5 Heat Kernel Asymptotics.- 6 Advanced Topics.- Part IV Applications.- 7 Shastic Processes.- 8 Applications in Mathematical Finance.- Summary.- References.- Index

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