LEADER 05078nam 22008415 450 001 9910972466503321 005 20250811111836.0 010 $a3-662-12616-8 024 7 $a10.1007/978-3-662-12616-5 035 $a(CKB)2660000000026944 035 $a(SSID)ssj0000899184 035 $a(PQKBManifestationID)11506680 035 $a(PQKBTitleCode)TC0000899184 035 $a(PQKBWorkID)10923567 035 $a(PQKB)10092576 035 $a(DE-He213)978-3-662-12616-5 035 $a(MiAaPQ)EBC3099793 035 $a(PPN)237998009 035 $a(EXLCZ)992660000000026944 100 $a20130321d1992 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aNumerical Solution of Stochastic Differential Equations /$fby Peter E. Kloeden, Eckhard Platen 205 $a1st ed. 1992. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d1992. 215 $a1 online resource (XXXVI, 636 p.) 225 1 $aStochastic Modelling and Applied Probability,$x2197-439X ;$v23 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a3-540-54062-8 311 08$a3-642-08107-X 320 $aIncludes bibliographical references and indexes. 327 $a1. Probability and Statistics -- 2. Probability and Stochastic Processes -- 3. Ito Stochastic Calculus -- 4. Stochastic Differential Equations -- 5. Stochastic Taylor Expansions -- 6. Modelling with Stochastic Differential Equations -- 7. Applications of Stochastic Differential Equations -- 8. Time Discrete Approximation of Deterministic Differential Equations -- 9. Introduction to Stochastic Time Discrete Approximation -- 10. Strong Taylor Approximations -- 11. Explicit Strong Approximations -- 12. Implicit Strong Approximations -- 13. Selected Applications of Strong Approximations -- 14. Weak Taylor Approximations -- 15. Explicit and Implicit Weak Approximations -- 16. Variance Reduction Methods -- 17. Selected Applications of Weak Approximations -- Solutions of Exercises -- Bibliographical Notes. 330 $aThe numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary. The book is also accessible to others who only require numerical recipes. The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable. To help the reader to develop an intuitive understanding of the underlying mathematics and hand-on numerical skills, exercises and over 100 PC-Exercises are included. 410 0$aStochastic Modelling and Applied Probability,$x2197-439X ;$v23 606 $aProbabilities 606 $aMathematical analysis 606 $aNumerical analysis 606 $aStatistics 606 $aMathematical physics 606 $aEngineering mathematics 606 $aEngineering$xData processing 606 $aProbability Theory 606 $aAnalysis 606 $aNumerical Analysis 606 $aStatistics in Business, Management, Economics, Finance, Insurance 606 $aTheoretical, Mathematical and Computational Physics 606 $aMathematical and Computational Engineering Applications 615 0$aProbabilities. 615 0$aMathematical analysis. 615 0$aNumerical analysis. 615 0$aStatistics. 615 0$aMathematical physics. 615 0$aEngineering mathematics. 615 0$aEngineering$xData processing. 615 14$aProbability Theory. 615 24$aAnalysis. 615 24$aNumerical Analysis. 615 24$aStatistics in Business, Management, Economics, Finance, Insurance. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aMathematical and Computational Engineering Applications. 676 $a519.2 700 $aKloeden$b Peter E$4aut$4http://id.loc.gov/vocabulary/relators/aut$021624 702 $aPlaten$b Eckhard$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910972466503321 996 $aNumerical solution of stochastic differential equations$91490331 997 $aUNINA