LEADER 03180nam 22005655 450 001 9910686792703321 005 20251202152615.0 010 $a9783031253263$b(electronic bk.) 010 $z9783031253256 024 7 $a10.1007/978-3-031-25326-3 035 $a(MiAaPQ)EBC7233236 035 $a(Au-PeEL)EBL7233236 035 $a(DE-He213)978-3-031-25326-3 035 $a(OCoLC)1375555639 035 $a(PPN)269658440 035 $a(CKB)26383681400041 035 $a(EXLCZ)9926383681400041 100 $a20230402d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 12$aA Course of Stochastic Analysis /$fby Alexander Melnikov 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (214 pages) 225 1 $aCMS/CAIMS Books in Mathematics,$x2730-6518 ;$v6 311 08$aPrint version: Melnikov, Alexander A Course of Stochastic Analysis Cham : Springer,c2023 9783031253256 320 $aIncludes bibliographical references and index. 327 $a1 Probabilistic Foundations -- 2 Random variables and their quantitative characteristics -- 3 Expectations and convergence of sequences of random variables -- 4 Weak convergence of sequences of random variables -- 5 Absolute continuity of probability measures and conditional expectations -- 6 Discrete time stochastic analysis: basic results -- 7 Discrete time stochastic analysis: further results and applications -- 8 Elements of classical theory of stochastic processes -- 9 Stochastic differential equations, diffusion processes and their applications -- 10 General theory of stochastic processes under ?usual conditions" -- 11 General theory of stochastic processes in applications -- 12 Supplementary problems -- References -- Index. 330 $aThe main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications. 410 0$aCMS/CAIMS Books in Mathematics,$x2730-6518 ;$v6 606 $aStochastic processes 606 $aProbabilities 606 $aStochastic Processes 606 $aProbability Theory 615 0$aStochastic processes. 615 0$aProbabilities. 615 14$aStochastic Processes. 615 24$aProbability Theory. 676 $a519.2 676 $a519.22 700 $aMelnikov$b Alexander$0150247 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910686792703321 996 $aA Course of Stochastic Analysis$93087636 997 $aUNINA