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The request for "Stochastic Process Doob" refers to the seminal 1953 textbook " Stochastic Processes
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- Measure-Theoretic Rigor: Before Doob, stochastic processes were treated informally. Doob placed them firmly in the Kolmogorov probability framework.
- Martingales: He formalized the concept of a martingale—a fair game where the expected future value equals the present value. This became the backbone of modern finance and filtration theory.
- Separability and Regularity: Doob introduced the concept of separable processes to handle the fact that continuous-time processes have uncountably many random variables. This fixed a major logical loophole in earlier probability theory.
What is a Stochastic Process?
