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007 cr nn 008mamaa
008 170213s2015 gw | s |||| 0|eng d
020 _a9783319262666
_9978-3-319-26266-6
024 7 _a10.1007/978-3-319-26266-6
_2doi
035 _ato000561036
040 _aSpringer
_cSpringer
_dRU-ToGU
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aAvramidi, Ivan G.
_eauthor.
_9469082
245 1 0 _aHeat Kernel Method and its Applications
_helectronic resource
_cby Ivan G. Avramidi.
250 _a1st ed. 2015.
260 _aCham :
_bSpringer International Publishing :
_bImprint: Birkhäuser,
_c2015.
300 _aXIX, 390 p. 17 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
505 0 _aPart 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 _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. .
650 0 _amathematics.
_9566183
650 0 _aPartial Differential Equations.
_9303602
650 1 4 _aMathematics.
_9566184
650 2 4 _aPartial Differential Equations.
_9303602
710 2 _aSpringerLink (Online service)
_9143950
773 0 _tSpringer eBooks
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-26266-6
912 _aZDB-2-SMA
999 _c416239