Wayson Kong

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7 Questions

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5	How fast does $\sum_{k=1}^n \frac{1}{k^\alpha}$ ( $\alpha\leq1$) diverge?
4	Is $B^{-1}-A^{-1}$ a positive definite matrix?
4	How to verify the following function is convex or not?
3	How to show $nP\{\|X\|>n\}\to 0$ as $n\to\infty$, but $X$ is not integrable.
3	Let $\{X_n\}$ be i.i.d integrable r.v.s, show that $\frac{1}{n}\max_{1\leq j\leq n}\|X_j\|\to 0 \quad \mbox{a.e.}$

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129 Reputation

+5	Let $\{X_n\}$ be i.i.d integrable r.v.s, show that $\frac{1}{n}\max_{1\leq j\leq n}\|X_j\|\to 0 \quad \mbox{a.e.}$
+10	Two random variable with the same variance and mean
+5	Is $\phi^T_tP_t^{-1}\phi_t\to 0$ when $P_{t+1}=\sum_{k=0}^t\phi_k\phi_k^T+P_0$?
+5	How fast does $\sum_{k=1}^n \frac{1}{k^\alpha}$ ( $\alpha\leq1$) diverge?

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2 Answers

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1	Two random variable with the same variance and mean
1	Evaluate limit with sum

13 Tags

1 limit	0 convergence × 3
1 measure-theory	0 probability × 3
1 probability-theory	0 matrices × 2
0 exercises-and-solutions × 4	0 linear-algebra × 2
0 homework × 3	0 sequences-and-series

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