03055nam 2200517 450 991068679270332120231204130720.09783031253263(electronic bk.)978303125325610.1007/978-3-031-25326-3(MiAaPQ)EBC7233236(Au-PeEL)EBL7233236(DE-He213)978-3-031-25326-3(OCoLC)1375555639(PPN)269658440(EXLCZ)992638368140004120230605d2023 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierA Course of Stochastic Analysis /Alexander Melnikov1st ed. 2023.Cham, Switzerland :Springer Nature Switzerland AG,[2023]©20231 online resource (214 pages)CMS/CAIMS Books in Mathematics Series ;Volume 6Print version: Melnikov, Alexander A Course of Stochastic Analysis Cham : Springer,c2023 9783031253256 Includes bibliographical references and index.1 Probabilistic Foundations -- 2 Random variables and their quantitative characteristics -- 3 Expectations and convergence of sequences of random variables -- 4 Weak convergence of sequences of random variables -- 5 Absolute continuity of probability measures and conditional expectations -- 6 Discrete time stochastic analysis: basic results -- 7 Discrete time stochastic analysis: further results and applications -- 8 Elements of classical theory of stochastic processes -- 9 Stochastic differential equations, diffusion processes and their applications -- 10 General theory of stochastic processes under ”usual conditions" -- 11 General theory of stochastic processes in applications -- 12 Supplementary problems -- References -- Index.The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.CMS/CAIMS books in mathematics ;Volume 6.Stochastic analysisAnàlisi estocàsticathubLlibres electrònicsthubStochastic analysis.Anàlisi estocàstica519.2Melnikov Alexander150247MiAaPQMiAaPQMiAaPQ9910686792703321A Course of Stochastic Analysis3087636UNINA