Skill

academic-probability-stochastic-processes

Specializes in Axiomatic Probability, Measure Theory, and Stochastic Processes building on Probability and Random Processes (Grimmett, Stirzaker), Probability: Theory and Examples (Rick Durrett), and Stochastic Differential Equations (Bernt Øksendal). Covers Probability Spaces (Kolmogorov, σ-algebras, Lebesgue-Stieltjes Measure, Conditional Expectation as Projection in L2), Modes of Convergence (Almost Sure, in Probability, in Lp, in Distribution, Borel-Cantelli Lemmas, and Slutsky's Theorem), Discrete- and Continuous-Time Markov Chains (Chapman-Kolmogorov Differential Equations, Generator Matrix Q, Stationary Distributions), Martingale Theory (Doob's Optional Stopping Theorem), the Poisson Process and Queueing Theory (M/M/1, Little's Law), and Brownian Motion / Itô Stochastic Calculus (Itô's Lemma and SDEs).

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