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020 _a9789819978793
_9978-981-99-7879-3
024 7 _a10.1007/978-981-99-7879-3
_2doi
050 4 _aQA274.2-.28
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
072 7 _aPBT
_2thema
072 7 _aPBWL
_2thema
100 1 _aParviainen, Mikko.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_971591
245 1 0 _aNotes on Tug-of-War Games and the p-Laplace Equation
_h[electronic resource] /
_cby Mikko Parviainen.
250 _a1st ed. 2024.
264 1 _aSingapore :
_bSpringer Nature Singapore :
_bImprint: Springer,
_c2024.
300 _aVIII, 76 p. 9 illus., 7 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringerBriefs on PDEs and Data Science,
_x2731-7609
505 0 _aChapter 1. Introduction -- Chapter 2. Viscosity Solutions -- Chapter 3. Stochastic Tug-of-War Game -- Chapter 4. Cancellation Method for Regularity of the Tug-of-War with Noise -- Chapter 5. Mean Value Characterizations -- Chapter 6. Further Regularity Methods -- Chapter 7. Open Problems and Comments.
520 _aThis book addresses the interplay between stochastic processes and partial differential equations. More specifically, it focuses on the connection between the nonlinear p-Laplace equation and the stochastic game called tug-of-war with noise. The connection in this context was discovered approximately 15 years ago and has since provided new insights and approaches. These lecture notes provide a brief but detailed and accessible introduction to the subject and to the more research-oriented literature. The book also presents the parabolic case side by side with the elliptic case, highlighting the fact that elliptic and parabolic equations are close in spirit in certain aspects. Moreover, it covers some parts of the regularity theory for these problems. Graduate students and advanced undergraduate students with a basic understanding of probability and partial differential equations will find this book useful.
650 0 _aStochastic analysis.
_959375
650 0 _aGame theory.
650 0 _aDifferential equations.
650 0 _aDiscrete mathematics.
650 1 4 _aStochastic Analysis.
_959375
650 2 4 _aGame Theory.
650 2 4 _aDifferential Equations.
650 2 4 _aDiscrete Mathematics.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9789819978786
776 0 8 _iPrinted edition:
_z9789819978809
830 0 _aSpringerBriefs on PDEs and Data Science,
_x2731-7609
_971592
856 4 0 _uhttps://doi.org/10.1007/978-981-99-7879-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c57819
_d57819