Question

Meaning of $ \lim_{n\rightarrow \infty} \Big|\frac{f_{D_n}(\eta_n)}{f_n(\eta_n)}-1 \Big|=0 \text{ wp approaching $1$}$

score 22 · Answer 1 · 2018-05-02 14:48:04

22

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Meaning of $ \lim_{n\rightarrow \infty} \Big|\frac{f_{D_n}(\eta_n)}{f_n(\eta_n)}-1 \Big|=0 \text{ wp approaching $1$}$

Published on 02 May 2018 - 14:48

score 426 · Answer 2 · 2026-03-25 06:05:46

426

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Convergence of $a_{n+2} = \sqrt{a_n} + \sqrt{a_{n+1}}$

Published on 25 Mar 2026 - 6:05

score 155 · Answer 3 · 2026-03-25 06:08:25

155

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Convergence of harmonic functions

Published on 25 Mar 2026 - 6:08

score 57 · Answer 4 · 2018-05-02 18:10:36

57

Views

Prove that $\sum^\infty_{n\text{ = }m}\big(\frac{a}{e^{n+b}}\big)=\frac{a\,e^{1-\,b\,-\,m}}{e-1}$

Published on 02 May 2018 - 18:10

score 67 · Answer 5 · 2026-03-26 10:43:32

67

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$X_n\leq Y_n+o_p(1)$ or $X_n\geq Y_n+o_p(1)$ imply $X_n$ converges to $Y_n$

Published on 26 Mar 2026 - 10:43

score 7.8k · Answer 6 · 2018-05-02 18:16:49

7.8k

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How do I determine if the series $ e^{-2n} $ converges or diverges? (From $ 0\to \infty $)

Published on 02 May 2018 - 18:16

score 1.8k · Answer 7 · 2018-05-02 22:56:01

1.8k

Views

This function seems to defy the integral test, where am I going wrong?

Published on 02 May 2018 - 22:56

score 144 · Answer 8 · 2026-03-25 15:39:46

144

Views

Random variables with rapidly varying tails

Published on 25 Mar 2026 - 15:39

score 140 · Answer 9 · 2018-05-03 02:02:03

140

Views

For which $\alpha$ does $\int_0^{\infty} \frac{\sin(x)}{x^{\alpha}}\,dx$ converge?

Published on 03 May 2018 - 2:02

score 407 · Answer 10 · 2026-03-25 06:06:31

407

Views

Bounded sequence $\{a_n\}_n$ such that $a_n < \frac{a_{n−1} + a_{n+1}}{2}$. Is $\{a_n\}_n$ convergent?

Published on 25 Mar 2026 - 6:06

score 363 · Answer 11 · 2026-03-28 17:40:26

363

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$X_n \rightarrow_{a.s.} X$ versus $X_n=X$ wpa 1

Published on 28 Mar 2026 - 17:40

score 39 · Answer 12 · 2026-03-25 16:02:24

39

Views

Prove $0 = E[e^{-M_{\infty}}] \to M_{\infty} = \infty$ a.s. w/ and then w/o Kolmogorov

Published on 25 Mar 2026 - 16:02

score 87 · Answer 13 · 2026-03-25 04:40:11

87

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Prove that following recursively defined sequence converges and its limit is 1/2

Published on 25 Mar 2026 - 4:40

score 84 · Answer 14 · 2026-03-27 22:53:05

84

Views

Proving the uniform convergence of $f_n$

Published on 27 Mar 2026 - 22:53

score 148 · Answer 15 · 2026-03-25 03:19:19

148

Views

Proving that a random walk using a maximum likelihood estimator can diverge to infinity

Published on 25 Mar 2026 - 3:19

List Question

Meaning of $ \lim_{n\rightarrow \infty} \Big|\frac{f_{D_n}(\eta_n)}{f_n(\eta_n)}-1 \Big|=0 \text{ wp approaching $1$}$

Convergence of $a_{n+2} = \sqrt{a_n} + \sqrt{a_{n+1}}$

Convergence of harmonic functions

Prove that $\sum^\infty_{n\text{ = }m}\big(\frac{a}{e^{n+b}}\big)=\frac{a\,e^{1-\,b\,-\,m}}{e-1}$

$X_n\leq Y_n+o_p(1)$ or $X_n\geq Y_n+o_p(1)$ imply $X_n$ converges to $Y_n$

How do I determine if the series $ e^{-2n} $ converges or diverges? (From $ 0\to \infty $)

This function seems to defy the integral test, where am I going wrong?

Random variables with rapidly varying tails

For which $\alpha$ does $\int_0^{\infty} \frac{\sin(x)}{x^{\alpha}}\,dx$ converge?

Bounded sequence $\{a_n\}_n$ such that $a_n < \frac{a_{n−1} + a_{n+1}}{2}$. Is $\{a_n\}_n$ convergent?

$X_n \rightarrow_{a.s.} X$ versus $X_n=X$ wpa 1

Prove $0 = E[e^{-M_{\infty}}] \to M_{\infty} = \infty$ a.s. w/ and then w/o Kolmogorov

Prove that following recursively defined sequence converges and its limit is 1/2

Proving the uniform convergence of $f_n$

Proving that a random walk using a maximum likelihood estimator can diverge to infinity

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