Heat Kernel Method and its Applications

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Sprache: Englisch

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Beschreibung

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.

Zusammenfassung

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

Inhaltsverzeichnis

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 Stochastic Processes.- 8 Applications in Mathematical Finance.- Summary.- References.- Index.

Details

Erscheinungsjahr:	2015
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Inhalt:	xix 390 S. 17 farbige Illustr. 390 p. 17 illus. in color.
ISBN-13:	9783319262659
ISBN-10:	3319262653
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Avramidi, Ivan
Auflage:	1st ed. 2015
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG
Maße:	241 x 160 x 28 mm
Von/Mit:	Ivan Avramidi
Erscheinungsdatum:	04.12.2015
Gewicht:	0,781 kg