A ground-breaking and practical treatment of probability and
stochastic processes
A Modern Theory of Random Variation 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.
In 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.
Throughout 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.
A Modern Theory of Random Variation 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.
Patrick Muldowney, Ph D, 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.
สารบัญ
Preface xi
Symbols xiii
1 Prologue 1
2 Introduction 37
3 Infinite-Dimensional Integration 83
4 Theory of the Integral 111
5 Random Variability 183
6 Gaussian Integrals 257
7 Brownian Motion 305
8 Stochastic Integration 383
9 Numerical Calculation 447
A Epilogue 491
Bibliography 505
Index 521
เกี่ยวกับผู้แต่ง
PATRICK MULDOWNEY, Ph D, served 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.
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