LEADER 02948oam 2200481 450 001 996418198903316 005 20210415135633.0 010 $a981-15-8864-3 024 7 $a10.1007/978-981-15-8864-8 035 $a(CKB)4100000011513691 035 $a(DE-He213)978-981-15-8864-8 035 $a(MiAaPQ)EBC6380824 035 $a(PPN)262174650 035 $a(EXLCZ)994100000011513691 100 $a20210415d2020 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aStochastic analysis /$fShigeo Kusuoka 205 $a1st ed. 2020. 210 1$aSingapore :$cSpringer,$d[2020] 210 4$d©2020 215 $a1 online resource (XII, 218 p. 1 illus.) 225 0 $aMonographs in Mathematical Economics,$x2364-8287 ;$vVolume 3 311 $a981-15-8863-5 327 $aChapter 1. Preparations from probability theory -- Chapter 2. Martingale with discrete parameter -- Chapter 3. Martingale with continuous parameter -- Chapter 4. Stochastic integral -- Chapter 5. Applications of stochastic integral -- Chapter 6. Stochastic differential equation -- Chapter 7. Application to finance -- Chapter 8. Appendices -- References. 330 $aThis book is intended for university seniors and graduate students majoring in probability theory or mathematical finance. In the first chapter, results in probability theory are reviewed. Then, it follows a discussion of discrete-time martingales, continuous time square integrable martingales (particularly, continuous martingales of continuous paths), stochastic integrations with respect to continuous local martingales, and stochastic differential equations driven by Brownian motions. In the final chapter, applications to mathematical finance are given. The preliminary knowledge needed by the reader is linear algebra and measure theory. Rigorous proofs are provided for theorems, propositions, and lemmas. In this book, the definition of conditional expectations is slightly different than what is usually found in other textbooks. For the Doob?Meyer decomposition theorem, only square integrable submartingales are considered, and only elementary facts of the square integrable functions are used in the proof. In stochastic differential equations, the Euler?Maruyama approximation is used mainly to prove the uniqueness of martingale problems and the smoothness of solutions of stochastic differential equations. . 410 0$aMonographs in Mathematical Economics,$x2364-8279 ;$v3 606 $aStochastic analysis 606 $aBusiness mathematics 615 0$aStochastic analysis. 615 0$aBusiness mathematics. 676 $a519.2 700 $aKusuoka$b Shigeo$060659 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a996418198903316 996 $aStochastic analysis$92547559 997 $aUNISA LEADER 01160nam0 22002893i 450 001 TO00574922 005 20231121125839.0 020 $aIT$b75-7229 100 $a20070214d1974 ||||0itac50 ba 101 | $aita 102 $ait 181 1$6z01$ai $bxxxe 182 1$6z01$an 200 1 $aCitta e sistemi urbani dell'Austria alpina$fFrancesco Adamo 210 $aTorino$cGiappichelli$d1974 215 $aX, 281 p.$cill.$d25 cm 300 $aIn testa al front.: Università degli Studi di Torino, Facoltà di Lettere e Filosofia, Istituto di Geografia. 700 1$aAdamo$b, Francesco$f <1941- >$3CFIV053492$4070$0555685 801 3$aIT$bIT-01$c20070214 850 $aIT-RM0460 $aIT-FR0017 899 $aBiblioteca Dell' Archivio Centrale Dello Stato$bRM0460 899 $aBiblioteca umanistica Giorgio Aprea$bFR0017 $eN 912 $aTO00574922 950 0$aBiblioteca umanistica Giorgio Aprea$d 52DMAB 103$e 52FLS0000300665 VMB RS $fA $h20181017$i20181017 977 $a 27$a 52 996 $aCittà e sistemi urbani dell'Austria Alpina$9982620 997 $aUNICAS