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I'm looking for a simple proof of the following fact, which is somehow Bernstein inequality in continuous time. Let $(M_t)_{t\geq 0}$ be a continuous local martingale. Then : $$P\left(\sup_{t\in [0,...

Consider the empirical and population CDF, $$ F_n(t) = \frac{1}{n} \sum_{i=1}^n 1\{X_i \leq t\} \quad \mbox{and} \quad F(t) = \mathbb{E} [F_n(t)], $$ where above $X_1, \dots, X_n$ are iid, real-...

Let $X_1, X_2, \dots, X_n$ be $n$ samples from a discrete-time continuous-space Markov Chain. Are there any good references who have provided a Chernoff-type bound regarding the behaviour of the ...