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| 001 | 978-3-032-01650-8 | ||
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_a10.1007/978-3-032-01650-8 _2doi |
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_aDalang, Robert C. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _923623 |
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| 245 | 1 | 0 |
_aStochastic Partial Differential Equations, Space-Time White Noise and Random Fields _h[electronic resource] / _cby Robert C. Dalang, Marta Sanz-Solé. |
| 250 | _a1st ed. 2026. | ||
| 264 | 1 |
_aCham : _bSpringer Nature Switzerland : _bImprint: Springer, _c2026. |
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_aXIX, 634 p. 1 illus. _bonline resource. |
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_atext _btxt _2rdacontent |
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_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_bTable of contents navigation _2onix |
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_bSingle logical reading order _2onix |
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_bShort alternative textual descriptions _2onix |
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_bUse of color is not sole means of conveying information _2onix |
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_bAll non-decorative content supports reading without sight _2onix |
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_atext file _bPDF _2rda |
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_aSpringer Monographs in Mathematics, _x2196-9922 |
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| 505 | 0 | _a1. Basics on Noise and SPDEs -- 2. Stochastic Integrals with Respect to Space-Time White Noise -- 3. Linear SPDEs Driven by Space-Time White Noise -- 4. Non-Linear SPDEs Driven by Space-Time White Noise -- 5. Asymptotic Behaviors in the Stochastic Heat Equation -- 6. Selected Results on SPDEs Driven by Space-Time White Noise. | |
| 506 | 0 | _aOpen Access | |
| 520 | _aThis open access book provides a comprehensive introduction to the theory of stochastic partial differential equations (SPDEs). The focus is on SPDEs driven by Gaussian space-time white noise. The book covers both linear and nonlinear SPDEs, with Lipschitz and locally Lipschitz coefficients and multiplicative noise. It provides a modern presentation of the theory of stochastic integration with respect to space-time white noise and unifies many results in the literature. The book discusses fundamental topics such as existence and uniqueness of random field solutions, along with their space-time sample path regularity properties. The book also presents a selection of additional topics such as weak solutions in law to SPDEs, space-time Markov properties, asymptotic bounds on moments, comparison theorems, a study of polarity of points for SPDEs with additive noise, and a study of SPDEs with rough initial conditions that includes the parabolic and hyperbolic Anderson models and their intermittency properties. In the context of the stochastic heat equation, the book discusses additional important topics including invariant and limit measures, reversible measures and their relationship to bridge measures, irreducibility properties, and large interval asymptotics. The appendices gather results from analysis and stochastic processes that are used throughout the core of the book, including key elements from the general theory of stochastic processes, a detailed presentation of Kolmogorov’s anisotropic continuity criterion, numerous integrability properties of the fundamental solutions and Green's functions associated to the heat and wave partial differential operators, explicit calculations of some space-time convolution series and some useful Gronwall-type lemmas. The book aims to be a reference for established researchers in the field of SPDEs, as well as for those who are interested in entering the field and becoming familiar with its techniques. In particular, graduate and postgraduate students with a background in stochastic analysis will find here a comprehensive and self-contained source of information which provides essential expertise in the subject. | ||
| 532 | 8 | _aAccessibility summary: This PDF has been created in accordance with the PDF/UA-1 standard to enhance accessibility, including screen reader support, described non-text content (images, graphs), bookmarks for easy navigation, keyboard-friendly links and forms and searchable, selectable text. We recognize the importance of accessibility, and we welcome queries about accessibility for any of our products. If you have a question or an access need, please get in touch with us at accessibilitysupport@springernature.com. Please note that a more accessible version of this eBook is available as ePub. | |
| 532 | 8 | _aNo reading system accessibility options actively disabled | |
| 532 | 8 | _aPublisher contact for further accessibility information: accessibilitysupport@springernature.com | |
| 650 | 0 |
_aMathematical analysis. _911388 |
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| 650 | 0 | _aStochastic analysis. | |
| 650 | 1 | 4 |
_aAnalysis. _911393 |
| 650 | 2 | 4 | _aStochastic Analysis. |
| 700 | 1 |
_aSanz-Solé, Marta. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut _923624 |
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| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer Nature eBook | |
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_iPrinted edition: _z9783032016492 |
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_iPrinted edition: _z9783032016515 |
| 776 | 0 | 8 |
_iPrinted edition: _z9783032016522 |
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_aSpringer Monographs in Mathematics, _x2196-9922 _923625 |
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| 856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-032-01650-8 |
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