Heat Kernel method and its applications / Ivan G. Avramidi

• Autore: Avramidi, Ivan G.
• Pubblicazione: [Cham], : Birkhäuser, : Springer, 2015
• Titolo uniforme: Heat Kernel method and its applications
• Descrizione fisica: XIX, 390 p. : ill. ; 24 cm
• Soggetto topico: 35-XX - Partial differential equations [MSC 2020]; 35K05 - Heat equation [MSC 2020]; 35K08 - Heat kernel [MSC 2020]; 35K10 - Second-order parabolic equations [MSC 2020]; 35K67 - Singular parabolic equations [MSC 2020]; 35Q91 - PDEs in connection with game theory, economics, social and behavioral sciences [MSC 2020]; 58-XX - Global analysis, analysis on manifolds [MSC 2020]; 58J05 - Elliptic equations on manifolds, general theory [MSC 2020]; 58J35 - Heat and other parabolic equation methods for PDEs on manifolds [MSC 2020]; 58J37 - Perturbations of PDEs on manifolds; asymptotics [MSC 2020]; 81Q20 - Semiclassical techniques including WKB and Maslov methods applied to problems in quantum theory [MSC 2020]; 91G20 - Derivative securities (option pricing, hedging, etc.) [MSC 2020]; 91G30 - Interest rates, asset pricing, etc. (stochastic models) [MSC 2020]; 91G80 - Financial applications of other theories [MSC 2020]
• Soggetto non controllato: Heat equations; Heat kernel; Partial Differential Equations; Semi-classical approximation; Singular Perturbations; Spectral asymptotics; Stochastic volatility models
• Nota di contenuto: 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.
• Titolo autorizzato: Heat Kernel method and its applications
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: VAN00113894
• Lo trovi qui: Univ. Vanvitelli
• Localizzazioni e accesso elettronico: http://dx.doi.org/10.1007/978-3-319-26266-6