LEADER 03252nam 22005175 450 001 9910254297603321 005 20200702014802.0 010 $a3-319-62226-9 024 7 $a10.1007/978-3-319-62226-2 035 $a(CKB)4340000000223261 035 $a(DE-He213)978-3-319-62226-2 035 $a(MiAaPQ)EBC6315052 035 $a(MiAaPQ)EBC5576604 035 $a(Au-PeEL)EBL5576604 035 $a(OCoLC)1012401151 035 $a(PPN)22125210X 035 $a(EXLCZ)994340000000223261 100 $a20171109d2017 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic Calculus $eAn Introduction Through Theory and Exercises /$fby Paolo Baldi 205 $a1st ed. 2017. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2017. 215 $a1 online resource (XIV, 627 p. 27 illus., 2 illus. in color.) 225 1 $aUniversitext,$x0172-5939 311 $a3-319-62225-0 320 $aIncludes bibliographical references and index. 327 $a1 Elements of probability -- 2 Stochastic processes -- 3 Brownian motion -- 4 Conditional probability -- 5 Martingales -- 6 Markov Processes -- 7 The stochastic integral -- 8 Stochastic calculus -- 9 Stochastic Differential Equations -- 10 PDE problems and diffusions -- 11 Simulation -- 12 Back to stochastic calculus -- 13 An application: finance -- Solutions of the exercises -- References -- Index. 330 $aThis book provides a comprehensive introduction to the theory of stochastic calculus and some of its applications. It is the only textbook on the subject to include more than two hundred exercises with complete solutions. After explaining the basic elements of probability, the author introduces more advanced topics such as Brownian motion, martingales and Markov processes. The core of the book covers stochastic calculus, including stochastic differential equations, the relationship to partial differential equations, numerical methods and simulation, as well as applications of stochastic processes to finance. The final chapter provides detailed solutions to all exercises, in some cases presenting various solution techniques together with a discussion of advantages and drawbacks of the methods used. Stochastic Calculus will be particularly useful to advanced undergraduate and graduate students wishing to acquire a solid understanding of the subject through the theory and exercises. Including full mathematical statements and rigorous proofs, this book is completely self-contained and suitable for lecture courses as well as self-study. 410 0$aUniversitext,$x0172-5939 606 $aProbabilities 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 615 0$aProbabilities. 615 14$aProbability Theory and Stochastic Processes. 676 $a519.2 700 $aBaldi$b Paolo$4aut$4http://id.loc.gov/vocabulary/relators/aut$042379 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910254297603321 996 $aStochastic Calculus$91562455 997 $aUNINA