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Theory and applications of Lévy processes (stochastic processes with stationary and independent increments): e.g. path properties, stochastic differential equations driven by jump-type processes, fluctuation theory of Lévy processes, queuing theory.
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Monotone convergence theorem for stochastic integrals
To add to the answer by JGWang: The MCT is useful beyond the DCT only when we do not know that the limit is integrable. But in this context, the MCT depends crucially on some form of nonnegativity so …