Question

For which values of $\alpha \geq 0$ is the function $\exp(\log^\alpha(x))$ varying regularly?

score 198 · Answer 1 · 2026-02-27 18:13:00

198

Views

For which values of $\alpha \geq 0$ is the function $\exp(\log^\alpha(x))$ varying regularly?

Published on 27 Feb 2026 - 18:13

score 550 · Answer 2 · 2026-02-27 18:12:03

550

Views

regular and slowly varying functions examples $e^{\log(x)}$, $e^{\lfloor \log(x) \rfloor}$, $2 + \sin(x)$ and $e^{(\log(x))^\beta}$

Published on 27 Feb 2026 - 18:12

score 1k · Answer 3 · 2026-02-27 18:08:58

1k

Views

Slowly varying function without limit at infinity

Published on 27 Feb 2026 - 18:08

score 217 · Answer 4 · 2026-03-20 22:33:01

217

Views

Is a nondecreasing function bounded by a slowly varying function also slowly varying?

Published on 20 Mar 2026 - 22:33

score 45 · Answer 5 · 2020-03-09 15:16:56

45

Views

Slowly varying functions and the direction of convergence

Published on 09 Mar 2020 - 15:16

score 55 · Answer 6 · 2020-06-08 21:41:13

55

Views

Are Quasi-Polynomial Time Functions Regularly Varying?

Published on 08 Jun 2020 - 21:41

score 141 · Answer 7 · 2020-06-21 13:28:40

141

Views

Examples of Continuous Probability Distributions with Slowly Varying Upper Tail and Infinite Expectation

Published on 21 Jun 2020 - 13:28

score 59 · Answer 8 · 2023-05-28 06:49:54

59

Views

Prove for monotone $L \colon (0, \infty) \to (0,\infty)$, $L$ is slowly-varying if and only if there exists $x$ such that $\frac{L(tx)}{L(t)} \to 1$

Published on 28 May 2023 - 6:49

score 34 · Answer 9 · 2023-06-09 02:25:47

34

Views

Prove $\exp(\int^x_0 \frac{U(t)}{t} dt)$ is reguarly varying (Extreme Values, Regular Variation and Point Processes)

Published on 09 Jun 2023 - 2:25

score 14 · Answer 10 · 2023-06-21 05:51:28

14

Views

If $\lim_{n \to \infty} \lambda_n U(a_n x) \to \chi(x)$, $U$ is regulary varying and $\frac{\chi(x)}{\chi(1)} = x^\rho$

Published on 21 Jun 2023 - 5:51

score 77 · Answer 11 · 2026-03-20 07:41:05

77

Views

Slowlying varying function with no limit at infinity: using Karamata representation theorem

Published on 20 Mar 2026 - 7:41

score 26 · Answer 12 · 2023-07-02 01:47:11

26

Views

Reguarly varying function and convergence in probability

Published on 02 Jul 2023 - 1:47

score 27 · Answer 13 · 2023-07-06 02:43:28

Prove $V$ is slowly-varying if $\frac{V(tx)-V(t)}{a(t)} \to \log x$ (excercise 0.4.3.1 in Extreme Values, Regular Variation and Point Processes)

score 39 · Answer 14 · 2023-12-11 12:00:28

39

Views

Product of power-law distributed random variables

Published on 11 Dec 2023 - 12:00

score 474 · Answer 15 · 2015-11-14 10:51:27

474

Views

Composite of slowly varying functions

Published on 14 Nov 2015 - 10:51

List Question

For which values of $\alpha \geq 0$ is the function $\exp(\log^\alpha(x))$ varying regularly?

regular and slowly varying functions examples $e^{\log(x)}$, $e^{\lfloor \log(x) \rfloor}$, $2 + \sin(x)$ and $e^{(\log(x))^\beta}$

Slowly varying function without limit at infinity

Is a nondecreasing function bounded by a slowly varying function also slowly varying?

Slowly varying functions and the direction of convergence

Are Quasi-Polynomial Time Functions Regularly Varying?

Examples of Continuous Probability Distributions with Slowly Varying Upper Tail and Infinite Expectation

Prove for monotone $L \colon (0, \infty) \to (0,\infty)$, $L$ is slowly-varying if and only if there exists $x$ such that $\frac{L(tx)}{L(t)} \to 1$

Prove $\exp(\int^x_0 \frac{U(t)}{t} dt)$ is reguarly varying (Extreme Values, Regular Variation and Point Processes)

If $\lim_{n \to \infty} \lambda_n U(a_n x) \to \chi(x)$, $U$ is regulary varying and $\frac{\chi(x)}{\chi(1)} = x^\rho$

Slowlying varying function with no limit at infinity: using Karamata representation theorem

Reguarly varying function and convergence in probability

Prove $V$ is slowly-varying if $\frac{V(tx)-V(t)}{a(t)} \to \log x$ (excercise 0.4.3.1 in Extreme Values, Regular Variation and Point Processes)

Product of power-law distributed random variables

Composite of slowly varying functions

Trending Questions

Popular # Hahtags

Popular Questions