LEADER 03957nam 22006854a 450 001 9910782193103321 005 20230617010653.0 010 $a1-282-19475-5 010 $a9786612194757 010 $a3-11-019929-7 024 7 $a10.1515/9783110199291 035 $a(CKB)1000000000520516 035 $a(EBL)325699 035 $a(OCoLC)232160032 035 $a(SSID)ssj0000149031 035 $a(PQKBManifestationID)11150962 035 $a(PQKBTitleCode)TC0000149031 035 $a(PQKBWorkID)10225090 035 $a(PQKB)10470783 035 $a(MiAaPQ)EBC325699 035 $a(DE-599)GBV58795177X 035 $a(DE-B1597)32450 035 $a(OCoLC)979970867 035 $a(DE-B1597)9783110199291 035 $a(Au-PeEL)EBL325699 035 $a(CaPaEBR)ebr10194821 035 $a(CaONFJC)MIL219475 035 $a(EXLCZ)991000000000520516 100 $a20030924d2003 uy 0 101 0 $aeng 135 $aurun#---|u||u 181 $ctxt 182 $cc 183 $acr 200 10$aError calculus for finance and physics$b[electronic resource] $ethe language of Dirichlet forms /$fby Nicolas Bouleau 210 $aBerlin ;$aNew York $cWalter de Gruyter$dc2003 215 $a1 online resource (244 p.) 225 1 $aDe Gruyter expositions in mathematics ;$v37 300 $aDescription based upon print version of record. 311 0 $a3-11-018036-7 320 $aIncludes bibliographical references and index. 327 $tFront matter --$tContents --$tChapter I Intuitive introduction to error structures --$tChapter II Strongly-continuous semigroups and Dirichlet forms --$tChapter III Error structures --$tChapter IV Images and products of error structures --$tChapter V Sensitivity analysis and error calculus --$tChapter VI Error structures on fundamental spaces space --$tChapter VII Application to financial models --$tChapter VIII Applications in the field of physics --$tBack matter 330 $aMany recent advances in modelling within the applied sciences and engineering have focused on the increasing importance of sensitivity analyses. For a given physical, financial or environmental model, increased emphasis is now placed on assessing the consequences of changes in model outputs that result from small changes or errors in both the hypotheses and parameters. The approach proposed in this book is entirely new and features two main characteristics. Even when extremely small, errors possess biases and variances. The methods presented here are able, thanks to a specific differential calculus, to provide information about the correlation between errors in different parameters of the model, as well as information about the biases introduced by non-linearity. The approach makes use of very powerful mathematical tools (Dirichlet forms), which allow one to deal with errors in infinite dimensional spaces, such as spaces of functions or stochastic processes. The method is therefore applicable to non-elementary models along the lines of those encountered in modern physics and finance. This text has been drawn from presentations of research done over the past ten years and that is still ongoing. The work was presented in conjunction with a course taught jointly at the Universities of Paris 1 and Paris 6. The book is intended for students, researchers and engineers with good knowledge in probability theory. 410 0$aGruyter expositions in mathematics ;$v37. 606 $aError analysis (Mathematics) 606 $aDirichlet forms 606 $aRandom variables 615 0$aError analysis (Mathematics) 615 0$aDirichlet forms. 615 0$aRandom variables. 676 $a511/.43 686 $aSK 820$2rvk 700 $aBouleau$b Nicolas$056550 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910782193103321 996 $aError calculus for finance and physics$93822741 997 $aUNINA