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Brownian motion, martingales, and stochastic calculus /[edited by] Jean-Francois Le Gall.
Switzerland : Springer, 2016
282 pages. : illustrations
Ký hiệu phân loại (DDC): 519.23
This book offers a rigorous and self-contained presentation of stochastic integration and stochastic calculus within the general framework of continuous semimartingales. The main tools of stochastic calculus, including Itô?s formula, the optional stopping theorem and Girsanov?s theorem, are treated in detail alongside many illustrative examples. The book also contains an introduction to Markov processes, with applications to solutions of stochastic differential equations and to connections between Brownian motion and partial differential equations. The theory of local times of semimartingales is discussed in the last chapter. Since its invention by Itô, stochastic calculus has proven to be one of the most important techniques of modern probability theory, and has been used in the most recent theoretical advances as well as in applications to other fields such as mathematical finance. Brownian Motion, Martingales, and Stochastic Calculus provides a strong theoretical background to the reader interested in such developments. Beginning graduate or advanced undergraduate students will benefit from this detailed approach to an essential area of probability theory. The emphasis is on concise and efficient presentation, without any concession to mathematical rigor. The material has been taught by the author for several years in graduate courses at two of the most prestigious French universities. The fact that proofs are given with full details makes the book particularly suitable for self-study. The numerous exercises help the reader to get acquainted with the tools of stochastic calculus.
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Game theory : a multi-leveled approach / Hans Peters
Heidelberg : Springer, 2015
493 pages. : illustrations
Ký hiệu phân loại (DDC): 519.3
This textbook presents the basics of game theory both on an undergraduate level and on a more advanced mathematical level. It is the second, revised version of the successful 2008 edition. The book covers most topics of interest in game theory, including cooperative game theory. Part I presents introductions to all these topics on a basic yet formally precise level. It includes chapters on repeated games, social
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Mathematics for economics and business / Ian Jacques
Harlow : FT Prentice Hall, 2006
tr. ; cm.
Ký hiệu phân loại (DDC): 512.02433
This market leading text is highly regarded by lecturers and students alike and has been praised for its informal, friendly style which helps students to understand and even enjoy their studies of mathematics. Assuming little prior knowledge of the subject, Mathematics for Economics and Business promotes self-study encouraging students to read and understand topics that can, at first, seem daunting. This text is suitable for undergraduate economics, business and accountancy students taking introductory level maths courses." "Key Features: Includes numerous applications and practice problems which help students appreciate maths as a tool used to analyse real economic and business problems. Solutions to all problems are included in the book. Topics are divided into one- or two-hour sessions which allow students to work at a realistic pace. Techniques needed to understand more advanced mathematics are carefully developed. Offers an excellent introduction to Excel and Maple." "New to this Edition: Brand new companion website containing additional material for both students and lecturers. New appendices on Implicit Differentiation and Hessian matrices for more advanced courses. Book jacket."--BOOK JACKET.
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