000 05800nam a22006735i 4500
001 978-3-032-01650-8
003 DE-He213
005 20260304124215.0
007 cr nn 008mamaa
008 260128s2026 sz | s |||| 0|eng d
020 _a9783032016508
_9978-3-032-01650-8
024 7 _a10.1007/978-3-032-01650-8
_2doi
050 4 _aQA299.6-433
072 7 _aPBK
_2bicssc
072 7 _aMAT034000
_2bisacsh
072 7 _aPBK
_2thema
082 0 4 _a515
_223
100 1 _aDalang, Robert C.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_923623
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.
300 _aXIX, 634 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
341 0 _bPDF/UA-1
_2onix
341 0 _bTable of contents navigation
_2onix
341 0 _bSingle logical reading order
_2onix
341 0 _bShort alternative textual descriptions
_2onix
341 0 _bUse of color is not sole means of conveying information
_2onix
341 0 _bUse of high contrast between text and background color
_2onix
341 0 _bNext / Previous structural navigation
_2onix
341 0 _bAll non-decorative content supports reading without sight
_2onix
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Monographs in Mathematics,
_x2196-9922
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
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
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783032016492
776 0 8 _iPrinted edition:
_z9783032016515
776 0 8 _iPrinted edition:
_z9783032016522
830 0 _aSpringer Monographs in Mathematics,
_x2196-9922
_923625
856 4 0 _uhttps://doi.org/10.1007/978-3-032-01650-8
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
912 _aZDB-2-SOB
999 _c579817
_d579817