LEADER 03855nam 22006135 450 001 9910886066103321 005 20260225113825.0 010 $a9783031631931 010 $a3031631935 024 7 $a10.1007/978-3-031-63193-1 035 $a(MiAaPQ)EBC31642118 035 $a(Au-PeEL)EBL31642118 035 $a(CKB)34775345900041 035 $a(MiAaPQ)EBC31643249 035 $a(Au-PeEL)EBL31643249 035 $a(DE-He213)978-3-031-63193-1 035 $a(OCoLC)1455132833 035 $a(EXLCZ)9934775345900041 100 $a20240903d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbability Theory II $eStochastic Calculus /$fby Andrea Pascucci 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (428 pages) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v166 311 08$a9783031631924 311 08$a3031631927 327 $a1 Stochastic processes -- 2 Markov processes -- 3 Continuous processes -- 4 Brownian motion -- 5 Poisson process -- 6 Stopping times -- 7 Strong Markov property -- 8 Continuous martingales -- 9 Theory of variation -- 10 Stochastic integral -- 11 Itô's formula -- 12 Multidimensional stochastic calculus -- 13 Change of measure and martingale representation -- 14 Stochastic differential equations -- 15 Feynman-Kac formulas -- 16 Linear stochastic equations -- 17 Strong solutions -- 18 Weak solutions -- 19 Complements.-20 A primer on parabolic PDEs. 330 $aThis book offers a modern approach to the theory of continuous-time stochastic processes and stochastic calculus. The content is treated rigorously, comprehensively, and independently. In the first part, the theory of Markov processes and martingales is introduced, with a focus on Brownian motion and the Poisson process. Subsequently, the theory of stochastic integration for continuous semimartingales was developed. A substantial portion is dedicated to stochastic differential equations, the main results of solvability and uniqueness in weak and strong sense, linear stochastic equations, and their relation to deterministic partial differential equations. Each chapter is accompanied by numerous examples. This text stems from over twenty years of teaching experience in stochastic processes and calculus within master's degrees in mathematics, quantitative finance, and postgraduate courses in mathematics for applications and mathematical finance at the University of Bologna. The book provides material for at least two semester-long courses in scientific studies (Mathematics, Physics, Engineering, Statistics, Economics, etc.) and aims to provide a solid background for those interested in the development of stochastic calculus theory and its applications. This text completes the journey started with the first volume of Probability Theory I - Random Variables and Distributions, through a selection of advanced classic topics in stochastic analysis. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v166 606 $aProbabilities 606 $aSocial sciences$xMathematics 606 $aProbability Theory 606 $aMathematics in Business, Economics and Finance 606 $aProbabilitats$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 0$aSocial sciences$xMathematics. 615 14$aProbability Theory. 615 24$aMathematics in Business, Economics and Finance. 615 7$aProbabilitats 676 $a519.2 700 $aPascucci$b Andrea$0475297 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910886066103321 996 $aProbability Theory II$94247174 997 $aUNINA