Stochastic processes are mathematical objects that describe the evolution of random systems over time. They have applications in a wide range of fields, including physics, finance, biology, and more. One of the foundational figures in the development of stochastic processes is John L. Doob, an American mathematician who made significant contributions to the field of probability theory.
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\usepackageamsmath, amssymb, bm \newcommand\E\mathbbE % Expectation \newcommand\P\mathbbP % Probability brew install --cask mactex Let’s be honest—reading Doob
brew install --cask mactex
Let’s be honest—reading Doob (1953) is brutal. The notation is dense, and the field has evolved. If you want the content without the pain, “install” these instead: here’s how to “install” it properly:
| If you want… | Get this PDF (legal preprints or library) | |--------------|-------------------------------------------| | A gentle intro to martingales | Probability with Martingales – David Williams | | Modern measure-theoretic probability | Probability and Stochastics – Erhan Çinlar | | Doob’s inequalities explained | Brownian Motion and Stochastic Calculus – Karatzas & Shreve (Chapter 1) | | Free and legal lecture notes | Stochastic Processes – statslab.cam.ac.uk (search for “Norris notes”) |
Once you have the file, here’s how to “install” it properly:
