An Advanced Course in Probability and Stochastic Processes (Kroese & Botev)
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Kroese and Botev build a rigorous account of probability from measurable spaces, integration, and random variables.
They compare different forms of convergence and develop the law of large numbers and central limit theorem.
Conditional expectation connects information and independence to Markov chains and other stochastic processes.
Martingales, stopping times, and Brownian motion reveal how random systems evolve over time.
The book brings these ideas together through stochastic integration, Itô calculus, and stochastic differential equations.
Read about the original source: An Advanced Course in Probability and Stochastic Processes
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