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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
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Almost sure convergence and asymptotic measurability
Let $(\Omega,\mathcal{A}, P)$ be a probability space and $X$ be a Borel measurable and separable map.
(i) $X_{n}\stackrel{\text{ as }}{\rightarrow}X$ and $\left(d\left(X_{n},X\right) \right)$ is asymp …