LEADER 05192nam 22007935 450 001 9910300255703321 005 20200705171059.0 010 $a1-4939-2867-8 024 7 $a10.1007/978-1-4939-2867-5 035 $a(CKB)3710000000521674 035 $a(SSID)ssj0001585572 035 $a(PQKBManifestationID)16264005 035 $a(PQKBTitleCode)TC0001585572 035 $a(PQKBWorkID)14865308 035 $a(PQKB)11738070 035 $a(DE-He213)978-1-4939-2867-5 035 $a(MiAaPQ)EBC6310754 035 $a(MiAaPQ)EBC5594786 035 $a(Au-PeEL)EBL5594786 035 $a(OCoLC)1076242166 035 $a(PPN)190532432 035 $a(EXLCZ)993710000000521674 100 $a20151118d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic Calculus and Applications /$fby Samuel N. Cohen, Robert J. Elliott 205 $a2nd ed. 2015. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2015. 215 $a1 online resource (XXIII, 666 p. 17 illus.) 225 1 $aProbability and Its Applications,$x2297-0371 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a1-4939-2866-X 320 $aIncludes bibliographical references and index. 327 $aPart I: Measure Theoretic Probability -- Measure Integral -- Probabilities and Expectation -- Part II: Stochastic Processes -- Filtrations, Stopping Times and Stochastic Processes -- Martingales in Discrete Time -- Martingales in Continuous Time -- The Classification of Stopping Times -- The Progressive, Optional and Predicable -Algebras -- Part III: Stochastic Integration -- Processes of Finite Variation -- The Doob-Meyer Decomposition -- The Structure of Square Integrable Martingales -- Quadratic Variation and Semimartingales -- The Stochastic Integral -- Random Measures -- Part IV: Stochastic Differential Equations -- Ito's Differential Rule -- The Exponential Formula and Girsanov's Theorem -- Lipschitz Stochastic Differential Equations -- Markov Properties of SDEs -- Weak Solutions of SDEs -- Backward Stochastic Differential Equations -- Part V: Applications -- Control of a Single Jump -- Optimal Control of Drifts and Jump Rates -- Filtering. Part VI: Appendices. 330 $aCompletely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to work with stochastic calculus as well as with its applications."?Zentralblatt (from review of the First Edition). 410 0$aProbability and Its Applications,$x2297-0371 606 $aProbabilities 606 $aDifferential equations, Partial 606 $aElectrical engineering 606 $aComputer science$xMathematics 606 $aEconomics, Mathematical 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aElectrical Engineering$3https://scigraph.springernature.com/ontologies/product-market-codes/T24000 606 $aComputational Mathematics and Numerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M1400X 606 $aQuantitative Finance$3https://scigraph.springernature.com/ontologies/product-market-codes/M13062 615 0$aProbabilities. 615 0$aDifferential equations, Partial. 615 0$aElectrical engineering. 615 0$aComputer science$xMathematics. 615 0$aEconomics, Mathematical. 615 14$aProbability Theory and Stochastic Processes. 615 24$aPartial Differential Equations. 615 24$aElectrical Engineering. 615 24$aComputational Mathematics and Numerical Analysis. 615 24$aQuantitative Finance. 676 $a519.2 700 $aCohen$b Samuel N$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755503 702 $aElliott$b Robert J$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300255703321 996 $aStochastic Calculus and Applications$92543324 997 $aUNINA