02948oam 2200481 450 99641819890331620210415135633.0981-15-8864-310.1007/978-981-15-8864-8(CKB)4100000011513691(DE-He213)978-981-15-8864-8(MiAaPQ)EBC6380824(PPN)262174650(EXLCZ)99410000001151369120210415d2020 uy 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierStochastic analysis /Shigeo Kusuoka1st ed. 2020.Singapore :Springer,[2020]©20201 online resource (XII, 218 p. 1 illus.) Monographs in Mathematical Economics,2364-8287 ;Volume 3981-15-8863-5 Chapter 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.This 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. .Monographs in Mathematical Economics,2364-8279 ;3Stochastic analysisBusiness mathematicsStochastic analysis.Business mathematics.519.2Kusuoka Shigeo60659MiAaPQMiAaPQUtOrBLWBOOK996418198903316Stochastic analysis2547559UNISA