I ordered this book when it was recommended by Amazon because I ordered the tape of Leonard Mlodinow  [["The Drunkard's Walk: How Randomness Rules Our Lives."]] It is a much more technical work, but is full of fascinating historical and physical asides. It is also full of profound and deep suggestions about time reversibility, bound states and lack thereof, and many other topics. At the same time the author has a wry humor. This starts with the title itself. A green and brown diffusion pattern adorns the cover (the previous edition had plaid), but the book is about Mr. Green of Green's theorem and Mr. Brown of Brownian motion. I can see now why Chern somewhat archly entitled one of his books "Complex Manifolds without Potential Theory: (With an Appendix on the Geometry of Characteristic Classes) (Universitext)." Chung's asides are often extremely funny and provocative. The style reminds me of Zee's books Fearful Symmetry: The Search for Beauty in Modern Physics (Princeton Science Library)'s" and "Quantum Field Theory in a Nutshell." I learned a great deal of relevance not only to quantum theory, statistical mechanics, and measure theory, but also about the background of options and derivatives trading in the stock market and the ensuing crashes. Both Brownian motion probability theory and the foundations of the Black-Scholes theorem trace back to the same French dissertation Louis Bachelier's Theory of Speculation: The Origins of Modern Finance in 1900. Chung carries this tale through Norbert Wiener Extrapolation, Interpolation, and Smoothing of Stationary Time Series, Kakutani Selected Papers: Vol. I (Contemporary Mathematicians), Doob Stochastic Processes (Wiley Classics Library), and the rest. He includes facimile reproductions of the title pages of the various classical papers in stochastic theory, theory of Brownian motion, etc. A great read and great fun.

Green, Brown, & Probability and Brownian Motion on the Line PDF

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