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Heat kernel method and its applications

Avramidi, Ivan G.

Heat kernel method and its applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Heat kernel method and its applicationsby Ivan G. Avramidi.
作者:	Avramidi, Ivan G.
出版者:	Cham :Springer International Publishing :2015.
面頁冊數:	xix, 390 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Differential equations, Partial.
電子資源:	http://dx.doi.org/10.1007/978-3-319-26266-6
ISBN:	9783319262666$q(electronic bk.)

Heat kernel method and its applications
Avramidi, Ivan G.

Heat kernel method and its applications[electronic resource] /by Ivan G. Avramidi. - Cham :Springer International Publishing :2015. - xix, 390 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783319262666$q(electronic bk.)

Standard No.: 10.1007/978-3-319-26266-6doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA374

Dewey Class. No.: 515.353

Heat kernel method and its applications
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505 0 $a 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.
520 $a 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.
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