Series: Lecture Notes in Mathematics , Vol. 1927
Subseries: Fondazione C.I.M.E., Firenze
2008, XI, 202 p. 22 illus., Softcover
ISBN: 978-3-540-75913-3
Due: December 5, 2007
About this book
This volume provides the texts of lectures given by L. Ambrosio, L. Caffarelli, M. Crandall, L.C. Evans, N. Fusco at the Summer course held in Cetraro (Italy) in 2005. These are introductory reports on current research by world leaders in the fields of calculus of variations and partial differential equations. The topics discussed are transport equations for nonsmooth vector fields, homogenization, viscosity methods for the infinite Laplacian, weak KAM theory and geometrical aspects of symmetrization. A historical overview of all CIME courses on the calculus of variations and partial differential equations is contributed by Elvira Mascolo.
Written for:
Researchers and graduate students
Table of contents
Series: Lecture Notes in Mathematics , Vol. 1929
2008, XVII, 393 p., Softcover
ISBN: 978-3-540-75872-3
Due: December 5, 2007
About this book
The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0<H<1/2 of Hurst index, the conditions of existence and uniqueness of solutions to SDE involving additive Wiener integrals, and of solutions of the mixed Brownian?fractional Brownian SDE. The author develops optimal filtering of mixed models including linear case, and studies financial applications and statistical inference with hypotheses testing and parameter estimation. She proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.
Written for:
Researchers and graduate students in probability theory, stochastic analysis, and financial mathematics
Table of contents
Series: Universitext
2008, XIV, 322 pp. 8 illus., Softcover
ISBN: 978-0-387-71275-8
Due: January 2008
About this textbook
Organizes material around theorems and proofs
Presentation is driven by detailed examples that illustrate how the subject works
Provides a background and history of the subject through interesting preliminary lectures
This textbook provides a rigorous and lucid introduction to the theory of ordinary differential equations (ODEs), which serve as mathematical models for many exciting real-world problems in science, engineering, and other disciplines.
Key Features of this textbook:
Effectively organizes the subject into easily manageable sections in the form of 42 class-tested lectures
Provides a theoretical treatment by organizing the material around theorems and proofs
Uses detailed examples to drive the presentation
Includes numerous exercise sets that encourage pursuing extensions of the material, each with an "answers or hints" section
Covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics
Provides excellent grounding and inspiration for future research contributions to the field of ODEs and related areas
This book is ideal for a senior undergraduate or a graduate-level course on ordinary differential equations. Prerequisites include a course in calculus.
Table of contents
2008, XV. 374 p., Hardcover
ISBN: 978-1-4020-6659-7
Due: December 7, 2007
About this book
Philosophers have long speculated that a link exists between natural numbers and the physical world:
Pythagoras "all is number"
John Dalton (1803) "Atoms combine in simple numerical ratios"
Proutfs hypothesis, published anonymously in 1815 "..the elements are different aggregates of the atoms of primordial hydrogen.."
Alexandre Emile Beguyer de Chancourtois (1862) "..the properties of the elements are the properties of numbers.."
William Harkins (1921) "the ratio Z/(A - Z) never exceeds the value 0.62 in atomic species"
Within this book, readers with an interest in mathematics, science or natural philosophy will find this expectation addressed............
Table of contents
Series: Universitext
2008, XXII, 501 p., Softcover
ISBN: 978-3-540-76269-0
Due: January 2008
About this textbook
Ideal basis for lectures, seminars, and crash courses on statistical applications in finance
Interactive approach using statistical software
Registration card supplied with the text is a valuable key to open doors that allows the use of the e-book version with links to world wide computing servers
Quite simply this is an essential text for anyone in the field of financial econometrics. Readers will find that, refreshingly, this text presents in a vivid yet concise style the necessary statistical and mathematical background for Financial Engineers.
It moves on to introduce the main ideas in mathematical finance and financial statistics.
For the second edition the book has been updated and extensively revised. Several new topics have been included, such as a chapter on credit risk management.
Topics covered are, among others, option valuation, financial time series analysis, value-at-risk, copulas, and statistics of the extremes.
The underlying structure of the book allows it to be used as a basis for lectures, seminars and even crash courses on the topic.
A full set of transparencies can be downloaded using the registration card at the back of the book.
The registration card also allows the use of the e-book version with links to world wide computing servers.
Table of contents
Option Pricing.- Statistical Model of Financial Time Series.- Selected Financial Applications.