03800nam 22006375 450 99619877380331620200630042313.03-319-02231-810.1007/978-3-319-02231-4(CKB)3710000000078594(DE-He213)978-3-319-02231-4(SSID)ssj0001067983(PQKBManifestationID)11600988(PQKBTitleCode)TC0001067983(PQKBWorkID)11094389(PQKB)10346204(MiAaPQ)EBC3107013(PPN)176105727(EXLCZ)99371000000007859420131114d2014 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierStrong and Weak Approximation of Semilinear Stochastic Evolution Equations[electronic resource] /by Raphael Kruse1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (XIV, 177 p. 4 illus.) Lecture Notes in Mathematics,0075-8434 ;2093Bibliographic Level Mode of Issuance: Monograph3-319-02230-X Introduction -- Stochastic Evolution Equations in Hilbert Spaces -- Optimal Strong Error Estimates for Galerkin Finite Element Methods -- A Short Review of the Malliavin Calculus in Hilbert Spaces -- A Malliavin Calculus Approach to Weak Convergence -- Numerical Experiments -- Some Useful Variations of Gronwall’s Lemma -- Results on Semigroups and their Infinitesimal Generators -- A Generalized Version of Lebesgue’s Theorem -- References -- Index.In this book we analyze the error caused by numerical schemes for the approximation of semilinear stochastic evolution equations (SEEq) in a Hilbert space-valued setting. The numerical schemes considered combine Galerkin finite element methods with Euler-type temporal approximations. Starting from a precise analysis of the spatio-temporal regularity of the mild solution to the SEEq, we derive and prove optimal error estimates of the strong error of convergence in the first part of the book. The second part deals with a new approach to the so-called weak error of convergence, which measures the distance between the law of the numerical solution and the law of the exact solution. This approach is based on Bismut’s integration by parts formula and the Malliavin calculus for infinite dimensional stochastic processes. These techniques are developed and explained in a separate chapter, before the weak convergence is proven for linear SEEq.Lecture Notes in Mathematics,0075-8434 ;2093Numerical analysisProbabilitiesPartial differential equationsNumerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Numerical analysis.Probabilities.Partial differential equations.Numerical Analysis.Probability Theory and Stochastic Processes.Partial Differential Equations.519.22Kruse Raphaelauthttp://id.loc.gov/vocabulary/relators/aut524888MiAaPQMiAaPQMiAaPQBOOK996198773803316Strong and weak approximation of semilinear stochastic evolution equations821251UNISA05381nam 2201393z- 450 991055759910332120210501(CKB)5400000000043686(oapen)https://directory.doabooks.org/handle/20.500.12854/69435(oapen)doab69435(EXLCZ)99540000000004368620202105d2020 |y 0engurmn|---annantxtrdacontentcrdamediacrrdacarrierApplication of the Systems Approach to the Management of Complex Water SystemsBasel, SwitzerlandMDPI - Multidisciplinary Digital Publishing Institute20201 online resource (314 p.)3-03943-769-0 3-03943-770-4 During the past five decades, we have witnessed a tremendous evolution in water resource system management. Three characteristics of this evolution are of particular note: First, the application of the systems approach to complex water management problems has been established as one of the most important advances in the field of water resource management. Second, the past five decades have brought a remarkable transformation of attitude in the water resource management community towards environmental concerns and action to address these concerns. Third, applying the principles of sustainability to water resource decision-making requires major changes in the objectives on which decisions are based, and an understanding of the complicated inter-relationships between existing ecological, economic, and social factors. The Special Issue includes 15 contributions that offer insights into contemporary problems, approaches, and issues related to the management of complex water resources systems. It will be presumptuous to say that these 15 contributions characterize the success or failure of the systems approach to support water resources decision-making. However, these contributions offer interesting lessons from current experiences and highlight possible future work.History of engineering and technologybicsscadaptive capacityagent-based modelingaggregation-decompositionANPartificial intelligenceartificial rechargeaveraging proceduresCanadaCHANSclimate changecommunitycomplex water systemcomplexitycoupled human-natural systemsdecision-makingdifferential equationsdisasterfreshwater resourcesfuzzy optimizationgroundwatergroup consensusgroup decision-support systemHEC-HMShuman-nature systemshuman-water systemshydro-sociologyhydrologyimpactimplementationinnovationintegrated urban watershed managementintegrated water resources managementItalyIWRMKashafroud watershedLim riverLim water systemsmachine learningmanagementmodeling perspectivesmodellingmulti-agent reinforcement learningmulti-purpose dammultiobjective optimisationmultireservoir operationsn/aneural networksoptimizationperceptionperformance-based engineeringplanningpolitical processesregional climate modelsreservoir operationreservoir-river systemresilienceriskrisk analysisriver abstractionSESsimulationsocial-ecological systemssocio-hydrologic modelingsocio-hydrologysociohydrologySoft Systemsstakeholderstochastic dynamic programmingSuDSsystem analysissystem dynamicssystemssystems analysessystems assessmenttreated wastewateruncertaintyuncertainty assessmentwater footprintwater managementwater policywater portfolio planningwater quantity-quality managementwater resource modellingwater resourceswater resources managementwater resources systemswine productionwinemaking sectorHistory of engineering and technologySimonovic Slobodan Pedt901413Simonovic Slobodan PothBOOK9910557599103321Application of the Systems Approach to the Management of Complex Water Systems3032069UNINA