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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

Consider $$D=|D|=\frac{\sum_{i=1}^n \sum_{j=1}^n I[|{\sqrt{T}}\hat\theta_{ij,T}|>f(n)]}{g(n)}, $$ where $i \ne j$, $I$ is the indicator function, $ |{\hat\theta_{ij,T}}|<1$, $f(n)=O(\ln(n))$, $g(n)=O …
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