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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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Wiener process related counterexample
The Wiener process is defined by the three properties:
1. $W(0) = 0$,
2. $W(t)$ is almost surely continuous, and
3. $W(t)$ has independent increments with $W(t) - W(s) \sim N(0, t-s)$ (for $0 ≤ s < …