LEADER 04158nam0 2200613 i 450 001 VAN00113894 005 20260626021805.24 017 70$2N$a9783319262666 035 40$a981670614 100 $a20180122d2015 |0itac50 ba 101 $aeng 102 $aCH 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aHeat Kernel method and its applications$fIvan G. Avramidi 210 $a[Cham]$cBirkhäuser$cSpringer$d2015 215 $aXIX, 390 p.$cill.$d24 cm 327 $aThe 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. 500 1$3VAN00235048$aHeat Kernel method and its applications$91522834 606 $a35-XX$xPartial differential equations [MSC 2020]$3VANC019763$2MF 606 $a35K05$xHeat equation [MSC 2020]$3VANC020092$2MF 606 $a35K08$xHeat kernel [MSC 2020]$3VANC033777$2MF 606 $a35K10$xSecond-order parabolic equations [MSC 2020]$3VANC022930$2MF 606 $a35K67$xSingular parabolic equations [MSC 2020]$3VANC033778$2MF 606 $a35Q91$xPDEs in connection with game theory, economics, social and behavioral sciences [MSC 2020]$3VANC033779$2MF 606 $a58-XX$xGlobal analysis, analysis on manifolds [MSC 2020]$3VANC019758$2MF 606 $a58J05$xElliptic equations on manifolds, general theory [MSC 2020]$3VANC023134$2MF 606 $a58J35$xHeat and other parabolic equation methods for PDEs on manifolds [MSC 2020]$3VANC024178$2MF 606 $a58J37$xPerturbations of PDEs on manifolds; asymptotics [MSC 2020]$3VANC022871$2MF 606 $a81Q20$xSemiclassical techniques including WKB and Maslov methods applied to problems in quantum theory [MSC 2020]$3VANC021228$2MF 606 $a91G20$xDerivative securities (option pricing, hedging, etc.) [MSC 2020]$3VANC031011$2MF 606 $a91G30$xInterest rates, asset pricing, etc. (stochastic models) [MSC 2020]$3VANC031012$2MF 606 $a91G80$xFinancial applications of other theories [MSC 2020]$3VANC031013$2MF 610 $aHeat equations$9KW:K 610 $aHeat kernel$9KW:K 610 $aPartial Differential Equations$9KW:K 610 $aSemi-classical approximation$9KW:K 610 $aSingular Perturbations$9KW:K 610 $aSpectral asymptotics$9KW:K 610 $aStochastic volatility models$9KW:K 620 $aCH$dCham$3VANL001889 700 1$aAvramidi$bIvan G.$3VANV087988$062541 712 $aBirkhäuser $3VANV108193$4650 712 $aSpringer $3VANV108073$4650 801 $aIT$bSOL$c20260703$gRICA 856 4 $uhttp://dx.doi.org/10.1007/978-3-319-26266-6$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00113894 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 0237 $e08eMF237 20180122 996 $aHeat Kernel method and its applications$91522834 997 $aUNICAMPANIA