{"product_id":"a-modern-theory-of-random-variation-isbn-9781118166406","title":"A Modern Theory of Random Variation","description":"\u003cp\u003e\u003cb\u003eA ground-breaking and practical treatment of probability and stochastic processes\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eA Modern Theory of Random Variation\u003c\/i\u003e is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions.\u003c\/p\u003e \u003cp\u003eIn place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals.\u003c\/p\u003e \u003cp\u003eThroughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eA Modern Theory of Random Variation\u003c\/i\u003e is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation.\u003c\/p\u003e \u003cp\u003ePatrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.\u003c\/p\u003e Preface xi\u003cbr\u003e\u003cbr\u003eSymbols xiii\u003cbr\u003e\u003cbr\u003e1 Prologue 1 \u003cp\u003e2 Introduction 37\u003c\/p\u003e \u003cp\u003e3 Infinite-Dimensional Integration 83\u003c\/p\u003e \u003cp\u003e4 Theory of the Integral 111\u003c\/p\u003e \u003cp\u003e5 Random Variability 183\u003c\/p\u003e \u003cp\u003e6 Gaussian Integrals 257\u003c\/p\u003e \u003cp\u003e7 Brownian Motion 305\u003c\/p\u003e \u003cp\u003e8 Stochastic Integration 383\u003c\/p\u003e \u003cp\u003e9 Numerical Calculation 447\u003c\/p\u003e \u003cp\u003eA Epilogue 491\u003cbr\u003e\u003cbr\u003eBibliography 505\u003cbr\u003e\u003cbr\u003eIndex 521\u003cbr\u003e\u003cbr\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePATRICK MULDOWNEY, PhD, \u003c\/b\u003eserved as lecturer in the Magee Business School at the University of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.\u003c\/p\u003e   \u003cp\u003e\u003cb\u003eA groundbreaking and practical treatment of probability and stochastic processes\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eA Modern Theory of Random Variation\u003c\/i\u003e presents a new and radical reformulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation based exclusively on finitely additive probability distribution functions.\u003c\/p\u003e \u003cp\u003eIn place of twentieth-century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals.\u003c\/p\u003e \u003cp\u003eDetailed numerical examples and demonstrations guide the reader through the abstract mathematical exposition. In addition, numerous diagrams and graphics provide vivid illustrations of the theory, from the elementary level to the more advanced.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eA Modern Theory of Random Variation\u003c\/i\u003e is suitable for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensable resource for researchers and practitioners who are seeking new concepts, techniques, and methodologies in data analysis, numerical calculation, and financial asset valuation.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47988638712037,"sku":"NP9781118166406","price":142.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118166406.jpg?v=1761781071","url":"https:\/\/k12savings.com\/es\/products\/a-modern-theory-of-random-variation-isbn-9781118166406","provider":"K12savings","version":"1.0","type":"link"}