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Results tagged with large-deviations
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user 23661
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A generalized Ballot theorem
Let $\{X_n\}_{n \in \mathbb{N}}$ be i.i.d. real random variables with $\mathbb{E}[X_i] = \mu \in \mathbb{R}$. Let $S_n = X_1 + X_2 + \cdots + X_n$.
Let $\nu \leq \mu$ be such that $\mathbb{P}[S_n < \ …
- 1,322
4
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Large deviations for sequences that are not sums of iid
Suppose $(S_n)_n$ is a sequence of real random variables. Denote their cumulant generating functions by $K_n(t) = \log\mathbb{E}\left[\mathrm{e}^{t S_n}\right]$, and assume that each $K_n$ is finite f …
- 1,322