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Results tagged with pr.probability
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user 27773
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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Looking for a citation for this simple generalization of the Markov bound to non-negative su...
Does anybody know a reference for the following theorem?
Theorem 1. Let $(X_t)_{t=0}^\infty$ be a non-negative supermartingale.
Then, for any constant $c > 0$, the event $(\exists
> t)\, X_t \ge c$ h …
- 183
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Chernoff-type bounds for a stopped sum of independent random variables
The two answers so far may give the impression that bounds in the desired spirit (Chernoff-like bounds for sums with stopping times) are not possible. But useful bounds in this spirit can indeed be s …
- 183
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Does Multiplicative Version of Azuma's Inequality Hold?
Yes, such bounds are possible. You can adapt the proof of Azuma's inequality to the multiplicative-error case, if you set it up correctly.
For example:
Lemma 10 [this paper].
Let $Y=\sum_{t=1}^T x_t …
- 183
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McDiarmid's Inequality bounding deviation with multiplicative error?
Fix $m$ arbitrary values $x_1, x_2, ..., x_m$ in $[0,1]$, and an integer $n$. Obtain $n$-set $S$ by drawing $n \le m$ times randomly without replacement from $\{1,2,..,m\}$. Define r.v. $X = \sum_{i …
- 183