Category:Doob's Maximal Inequality
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This category contains pages concerning Doob's Maximal Inequality:
Discrete Time
Let $\struct {\Omega, \Sigma, \sequence {\FF_n}_{n \mathop \ge 0}, \Pr}$ be a filtered probability space.
Let $\sequence {X_n}_{n \mathop \ge 0}$ be a non-negative $\sequence {\FF_n}_{n \mathop \ge 0}$-submartingale.
Let:
- $\ds X_n^\ast = \max_{0 \mathop \le k \mathop \le n} X_k$
where $\max$ is the pointwise maximum.
Let $\lambda > 0$.
Then:
- $\lambda \map \Pr {X_n^\ast \ge \lambda} \le \expect {X_n}$
Pages in category "Doob's Maximal Inequality"
The following 8 pages are in this category, out of 8 total.