000			a
999			_c31036 _d31036
008			220609b xxu||||| |||| 00| 0 eng d
020			_a9789811588662
082			_a519.22 _bKUS
100			_aKusuoka, Shigeo
245			_aStochastic analysis
260			_bSpringer, _c2020 _aSingapore :
300			_axii, 218 p. ; _bill., _c23 cm
365			_b34.99 _cEUR _d86.00
490			_aMonographs in Mathematical Economics _vv.3
504			_aIncludes bibliographical references and index.
520			_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.
650			_aMathematical Economic
650			_aStochastic Analysis
650			_aMonographs
942			_2ddc _cBK