Stochastic Analysis

Author: Hiroyuki Matsumoto
Publisher: Cambridge University Press
ISBN: 1108107885
Format: PDF, ePub, Mobi
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Thanks to the driving forces of the Itô calculus and the Malliavin calculus, stochastic analysis has expanded into numerous fields including partial differential equations, physics, and mathematical finance. This book is a compact, graduate-level text that develops the two calculi in tandem, laying out a balanced toolbox for researchers and students in mathematics and mathematical finance. The book explores foundations and applications of the two calculi, including stochastic integrals and differential equations, and the distribution theory on Wiener space developed by the Japanese school of probability. Uniquely, the book then delves into the possibilities that arise by using the two flavors of calculus together. Taking a distinctive, path-space-oriented approach, this book crystallizes modern day stochastic analysis into a single volume.

Introduction to Stochastic Analysis

Author: Vigirdas Mackevicius
Publisher: John Wiley & Sons
ISBN: 1118603249
Format: PDF, ePub
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This is an introduction to stochastic integration and stochastic differential equations written in an understandable way for a wide audience, from students of mathematics to practitioners in biology, chemistry, physics, and finances. The presentation is based on the naïve stochastic integration, rather than on abstract theories of measure and stochastic processes. The proofs are rather simple for practitioners and, at the same time, rather rigorous for mathematicians. Detailed application examples in natural sciences and finance are presented. Much attention is paid to simulation diffusion processes. The topics covered include Brownian motion; motivation of stochastic models with Brownian motion; Itô and Stratonovich stochastic integrals, Itô’s formula; stochastic differential equations (SDEs); solutions of SDEs as Markov processes; application examples in physical sciences and finance; simulation of solutions of SDEs (strong and weak approximations). Exercises with hints and/or solutions are also provided.

Survival and Event History Analysis

Author: Odd Aalen
Publisher: Springer Science & Business Media
ISBN: 038768560X
Format: PDF, ePub, Mobi
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The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. The book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.

Strength from Weakness Structural Consequences of Weak Interactions in Molecules Supermolecules and Crystals

Author: Aldo Domenicano
Publisher: Springer Science & Business Media
ISBN: 940100546X
Format: PDF, ePub, Mobi
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The accurate determination of the structure of molecular systems provides information about the consequences of weak interactions both within and between molecules. These consequences impact the properties of the materials and the behaviour in interactions with other substances. The book presents modern experimental and computational techniques for the determination of molecular structure. It also highlights applications ranging from the simplest molecules to DNA and industrially significant materials. Readership: Graduate students and researchers in structural chemistry, computational chemistry, molecular spectroscopy, crystallography, supramolecular chemistry, solid state chemistry and physics, and materials science.

On the Power of Fuzzy Markup Language

Author: Giovanni Acampora
Publisher: Springer
ISBN: 3642354882
Format: PDF, Docs
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One of the most successful methodology that arose from the worldwide diffusion of Fuzzy Logic is Fuzzy Control. After the first attempts dated in the seventies, this methodology has been widely exploited for controlling many industrial components and systems. At the same time, and very independently from Fuzzy Logic or Fuzzy Control, the birth of the Web has impacted upon almost all aspects of computing discipline. Evolution of Web, Web2.0 and Web 3.0 has been making scenarios of ubiquitous computing much more feasible; consequently information technology has been thoroughly integrated into everyday objects and activities. What happens when Fuzzy Logic meets Web technology? Interesting results might come out, as you will discover in this book. Fuzzy Mark-up Language is a son of this synergistic view, where some technological issues of Web are re-interpreted taking into account the transparent notion of Fuzzy Control, as discussed here. The concept of a Fuzzy Control that is conceived and modeled in terms of a native web wisdom represents another step towards the last picture of Pervasive Web Intelligence.

Discrete Harmonic Analysis

Author: Tullio Ceccherini-Silberstein
Publisher: Cambridge University Press
ISBN: 1107182336
Format: PDF, ePub, Mobi
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A self-contained introduction to discrete harmonic analysis with an emphasis on the Discrete and Fast Fourier Transforms.