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Here I would like to share some selected notes that I wrote along my path of mathematical learning and research over the past years. Most of the topics are classical and fundamental. This is mainly for the benefit of students.
The Mathematical Theory of Moment Generating Functions
The Wiener-Itô Chaos Decomposition and Multiple Wiener Integrals
Integration on Groups and Non-abelian Fourier Analysis
An Introductory Course on Stochastic Calculus
An Introduction to the Theory of Rough Paths