| 000 | 03739nam a22005415i 4500 | ||
|---|---|---|---|
| 001 | 978-3-031-69586-5 | ||
| 003 | DE-He213 | ||
| 005 | 20251030112921.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 240830s2024 sz | s |||| 0|eng d | ||
| 020 |
_a9783031695865 _9978-3-031-69586-5 |
||
| 024 | 7 |
_a10.1007/978-3-031-69586-5 _2doi |
|
| 050 | 4 | _aQA274-274.9 | |
| 072 | 7 |
_aPBT _2bicssc |
|
| 072 | 7 |
_aPBWL _2bicssc |
|
| 072 | 7 |
_aMAT029000 _2bisacsh |
|
| 072 | 7 |
_aPBT _2thema |
|
| 072 | 7 |
_aPBWL _2thema |
|
| 100 | 1 |
_aGoodair, Daniel. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _983215 |
|
| 245 | 1 | 0 |
_aStochastic Calculus in Infinite Dimensions and SPDEs _h[electronic resource] / _cby Daniel Goodair, Dan Crisan. |
| 250 | _a1st ed. 2024. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2024. |
|
| 300 |
_aX, 136 p. _bonline resource. |
||
| 336 |
_atext _btxt _2rdacontent |
||
| 337 |
_acomputer _bc _2rdamedia |
||
| 338 |
_aonline resource _bcr _2rdacarrier |
||
| 347 |
_atext file _bPDF _2rda |
||
| 490 | 1 |
_aSpringerBriefs in Mathematics, _x2191-8201 |
|
| 505 | 0 | _a1 Introduction -- 2 Stochastic Calculus in Infinite Dimensions -- 3 Stochastic Differential Equations in Infinite Dimensions -- 4 A Toolbox for Nonlinear SPDEs -- 5 Existence Theory for Nonlinear SPDEs and the Stochastic Navier-Stokes Equations -- A Appendix -- References -- Index . | |
| 520 | _aIntroducing a groundbreaking framework for stochastic partial differential equations (SPDEs), this work presents three significant advancements over the traditional variational approach. Firstly, Stratonovich SPDEs are explicitly addressed. Widely used in physics, Stratonovich SPDEs have typically been converted to Ito form for mathematical treatment. While this conversion is understood heuristically, a comprehensive treatment in infinite dimensions has been lacking, primarily due to insufficient rigorous results on martingale properties. Secondly, the framework incorporates differential noise, assuming the noise operator is only bounded from a smaller Hilbert space into a larger one, rather than within the same space. This necessitates additional regularity in the Ito form to solve the original Stratonovich SPDE. This aspect has been largely overlooked, despite the increasing popularity of gradient-dependent Stratonovich noise in fluid dynamics and regularisation by noise studies. Lastly, the framework departs from the explicit duality structure (Gelfand Triple), which is typically expected in the study of analytically strong solutions. This extension builds on the classical variational framework established by Röckner and Pardoux, advancing it in all three key aspects. Explore this innovative approach that not only addresses existing challenges but also opens new avenues for research and application in SPDEs. . | ||
| 650 | 0 |
_aStochastic processes. _976770 |
|
| 650 | 0 |
_aCalculus. _983216 |
|
| 650 | 1 | 4 |
_aStochastic Calculus. _983217 |
| 700 | 1 |
_aCrisan, Dan. _eauthor. _0(orcid)0000-0003-1486-1517 _1https://orcid.org/0000-0003-1486-1517 _4aut _4http://id.loc.gov/vocabulary/relators/aut _983218 |
|
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031695858 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031695872 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783031695889 |
| 830 | 0 |
_aSpringerBriefs in Mathematics, _x2191-8201 _970788 |
|
| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-031-69586-5 |
| 912 | _aZDB-2-SMA | ||
| 912 | _aZDB-2-SXMS | ||
| 999 |
_c62876 _d62876 |
||