Uncertainty, Intuition and Expectation.- Expectation.- Probability.- Some Basic Models.- Conditioning.- Applications of the Independence Concept.- The Two Basic Limit Theorems.- Continuous Random Variables and Their Transformations.- Markov Processes in Discrete Time.- Markov Processes in Continuous Time.- Action Optimisation: Dynamic Programming.- Optimal Resource Allocation.- Finance: Option Pricing and the Implied Martingale.- Second-Order Theory.- Consistency and Extension: The Finite-Dimensional Case.- Stochastic Convergence.- Martingales.- Extension: Examples of the Infinite-Dimensional Case.- Large-Deviation Theory.- Quantum Mechanics.
4th edition
From the reviews of the fourth edition: "... a clear success in its unorthodoxy, Probability via Expectation has become a treasured classic." P.A.L. Emrechts in "Short Book Reviews", Vol. 21/1, April, 2001 "Apart from presenting a case for the development of probability theory by using the expectation operator rather than probability measure as the primitive notion, a second distinctive feature of this book is the very large range of modern applications that it covers. Many of these are addressed by more than 350 exercises interspersed throughout the text. In summary, this well written book is a ! introduction to probability theory and its applications." (Norbert Henze, Metrika, November, 2002) "Originally published in 1970, this book has stood the test of time. ! the text demonstrates a modern alternative approach to a now classical field. ! The fourth edition contains a number of modifications and corrections. New material on dynamic programming, optimal allocation, options pricing and large deviations is included." (Martin T. Wells, Journal of the American Statistical Association, September 2001)
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