LEADER 03819nam 22007335 450 001 9910983315803321 005 20250915141622.0 010 $a9783031750236$b(electronic bk.) 010 $z9783031750229 024 7 $a10.1007/978-3-031-75023-6 035 $a(MiAaPQ)EBC31887331 035 $a(Au-PeEL)EBL31887331 035 $a(CKB)37345597800041 035 $a(DE-He213)978-3-031-75023-6 035 $a(OCoLC)1492991330 035 $a(EXLCZ)9937345597800041 100 $a20250123d2025 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumerical Methods for Extreme Responses of Dynamical Systems $eFinite Dimensional Models /$fby Mircea D. Grigoriu 205 $a1st ed. 2025. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2025. 215 $a1 online resource (619 pages) 311 08$aPrint version: Grigoriu, Mircea D. Numerical Methods for Extreme Responses of Dynamical Systems Cham : Springer,c2025 9783031750229 327 $aIntroduction.-, Primer of probability theory -- , Random vectors and processes -- , Convergence of random elements -- , Extremes of random processes by finite dimensional (FD) models -- , Extremes of solutions of stochastic differential equations by finite dimensional (FD) models. 330 $aThis book constructs input finite dimensional (FD) models that are amendable for numerical calculations and provides accurate representations for responses of dynamical systems to these inputs, i.e., numerical solutions of stochastic equations. It establishes conditions under which numerical solutions of these equations deliver accurate estimates of extreme responses of dynamical systems that are needed to, for example, predict extreme weather events and design reliable aircrafts. It is intended to serve a broad audience including graduate students, researchers, engineers, scientists and applied mathematicians interested in the formulation and solutions of complex stochastic problems. Includes algorithms for constructing FD models for a broad range of inputs and generating realizations of these models; Uses data-based estimates of extremes of outputs of stochastic equations based on high/low fidelity numerical solutions; Gives practical criteria for the convergence of numerical estimates of extreme system responses. 606 $aStochastic analysis 606 $aStochastic processes 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aStochastic Analysis 606 $aStochastic Processes 606 $aStochastic Systems and Control 606 $aEngineering Mathematics 606 $aMathematical and Computational Engineering Applications 606 $aAnālisi estocāstica$2thub 606 $aProcessos estocāstics$2thub 606 $aEnginyeria$2thub 606 $aProcessament de dades$2thub 608 $aLlibres electrōnics$2thub 615 0$aStochastic analysis. 615 0$aStochastic processes. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 14$aStochastic Analysis. 615 24$aStochastic Processes. 615 24$aStochastic Systems and Control. 615 24$aEngineering Mathematics. 615 24$aMathematical and Computational Engineering Applications. 615 7$aAnālisi estocāstica 615 7$aProcessos estocāstics 615 7$aEnginyeria 615 7$aProcessament de dades 676 $a519.22 700 $aGrigoriu$b Mircea D$0148085 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910983315803321 996 $aNumerical Methods for Extreme Responses of Dynamical Systems$94316310 997 $aUNINA