000 | 03030nam a22004335i 4500 | ||
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001 | vtls000561036 | ||
003 | RU-ToGU | ||
005 | 20210922090532.0 | ||
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 |
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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 |