MEASURES INTEGRALS AND MARTINGALES

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Measures Integrals And Martingales

Author : René L. Schilling
ISBN : 0521850150
Genre : Mathematics
File Size : 80.27 MB
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This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability.
Category: Mathematics

Measures Integrals And Martingales

Author : Ren L. Schilling
ISBN : 9781316620243
Genre : Mathematics
File Size : 26.30 MB
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A concise, elementary introduction to measure and integration theory, requiring few prerequisites as theory is developed quickly and simply.
Category: Mathematics

From Measures To It Integrals

Author : Ekkehard Kopp
ISBN : 9781139497718
Genre : Mathematics
File Size : 42.8 MB
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From Measures to Itô Integrals gives a clear account of measure theory, leading via L2-theory to Brownian motion, Itô integrals and a brief look at martingale calculus. Modern probability theory and the applications of stochastic processes rely heavily on an understanding of basic measure theory. This text is ideal preparation for graduate-level courses in mathematical finance and perfect for any reader seeking a basic understanding of the mathematics underpinning the various applications of Itô calculus.
Category: Mathematics

Exercises In Analysis

Author : Leszek Gasińksi
ISBN : 9783319061764
Genre : Mathematics
File Size : 49.24 MB
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Exercises in Analysis will be published in two volumes. This first volume covers problems in five core topics of mathematical analysis: metric spaces; topological spaces; measure, integration and Martingales; measure and topology and functional analysis. Each of five topics correspond to a different chapter with inclusion of the basic theory and accompanying main definitions and results, followed by suitable comments and remarks for better understanding of the material. At least 170 exercises/problems are presented for each topic, with solutions available at the end of each chapter. The entire collection of exercises offers a balanced and useful picture for the application surrounding each topic. This nearly encyclopedic coverage of exercises in mathematical analysis is the first of its kind and is accessible to a wide readership. Graduate students will find the collection of problems valuable in preparation for their preliminary or qualifying exams as well as for testing their deeper understanding of the material. Exercises are denoted by degree of difficulty. Instructors teaching courses that include one or all of the above-mentioned topics will find the exercises of great help in course preparation. Researchers in analysis may find this Work useful as a summary of analytic theories published in one accessible volume.
Category: Mathematics

Random And Vector Measures

Author : M. M. Rao
ISBN : 9789814350822
Genre : Electronic books
File Size : 40.45 MB
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The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. The spaces can be Banach or Frechet types. Several stationary aspects and related processes are analyzed whilst numerous new results are included and many research avenues are opened up.
Category: Electronic books

Measure Probability And Mathematical Finance

Author : Guojun Gan
ISBN : 9781118831960
Genre : Business & Economics
File Size : 20.61 MB
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An introduction to the mathematical theory and financial models developed and used on Wall Street Providing both a theoretical and practical approach to the underlying mathematical theory behind financial models, Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach presents important concepts and results in measure theory, probability theory, stochastic processes, and stochastic calculus. Measure theory is indispensable to the rigorous development of probability theory and is also necessary to properly address martingale measures, the change of numeraire theory, and LIBOR market models. In addition, probability theory is presented to facilitate the development of stochastic processes, including martingales and Brownian motions, while stochastic processes and stochastic calculus are discussed to model asset prices and develop derivative pricing models. The authors promote a problem-solving approach when applying mathematics in real-world situations, and readers are encouraged to address theorems and problems with mathematical rigor. In addition, Measure, Probability, and Mathematical Finance features: A comprehensive list of concepts and theorems from measure theory, probability theory, stochastic processes, and stochastic calculus Over 500 problems with hints and select solutions to reinforce basic concepts and important theorems Classic derivative pricing models in mathematical finance that have been developed and published since the seminal work of Black and Scholes Measure, Probability, and Mathematical Finance: A Problem-Oriented Approach is an ideal textbook for introductory quantitative courses in business, economics, and mathematical finance at the upper-undergraduate and graduate levels. The book is also a useful reference for readers who need to build their mathematical skills in order to better understand the mathematical theory of derivative pricing models.
Category: Business & Economics

Mathematical Reviews

Author :
ISBN : UOM:39015078588624
Genre : Mathematics
File Size : 36.51 MB
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Category: Mathematics

L Vy Processes And Stochastic Calculus

Author : David Applebaum
ISBN : 0521832632
Genre : Mathematics
File Size : 66.53 MB
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Graduate text decsribing two of the main tools for modern mathematical finance.
Category: Mathematics

Estimation And Control Problems For Stochastic Partial Differential Equations

Author : Pavel S. Knopov
ISBN : 9781461482864
Genre : Mathematics
File Size : 69.75 MB
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Focusing on research surrounding aspects of insufficiently studied problems of estimation and optimal control of random fields, this book exposes some important aspects of those fields for systems modeled by stochastic partial differential equations. It contains many results of interest to specialists in both the theory of random fields and optimal control theory who use modern mathematical tools for resolving specific applied problems, and presents research that has not previously been covered. More generally, this book is intended for scientists, graduate, and post-graduates specializing in probability theory and mathematical statistics. The models presented describe many processes in turbulence theory, fluid mechanics, hydrology, astronomy, and meteorology, and are widely used in pattern recognition theory and parameter identification of stochastic systems. Therefore, this book may also be useful to applied mathematicians who use probability and statistical methods in the selection of useful signals subject to noise, hypothesis distinguishing, distributed parameter systems optimal control, and more. Material presented in this monograph can be used for education courses on the estimation and control theory of random fields.
Category: Mathematics