A Modern Theory of Random Variation

A ground-breaking and practical treatment of probability andstochastic processes A Modern Theory of Random Variation is a new and radicalre-formulation of the mathematical underpinnings of subjects asdiverse as investment, communication engineering, and quantummechanics. Setting aside the classical theory of probabilitymeasure spaces, the book utilizes a mathematically rigorous versionof the theory of random variation that bases itself exclusively onfinitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measuretheory, the author uses the simpler concept of Riemann sums, andthe non-absolute Riemann-type integration of Henstock. Readers aresupplied with an accessible approach to standard elements ofprobability theory such as the central limmit theorem and Brownianmotion as well as remarkable, new results on Feynman diagrams andstochastic integrals. Throughout the book, detailed numerical demonstrations accompanythe discussions of abstract mathematical theory, from the simplestelements of the subject to the most complex. In addition, an arrayof numerical examples and vivid illustrations showcase how thepresented methods and applications can be undertaken at variouslevels of complexity. A Modern Theory of Random Variation is a suitable bookfor courses on mathematical analysis, probability theory, andmathematical finance at the upper-undergraduate and graduatelevels. The book is also an indispensible resource for researchersand practitioners who are seeking new concepts, techniques andmethodologies in data analysis, numerical calculation, andfinancial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee BusinessSchool 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 randomvariation.