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A bit of a newbie question, but what exactly does tilde mean in this case?

$$P(X>x) ∼ Cx^{−α}$$

This is in a context of some distribution (say Gaussian) that has Paretian tails.

I have seen this notation a lot in the probability theory, but I do not think I am very clear about its meaning.

EDIT:

So if the ratio of the two goes to $1$ as $x \rightarrow \infty$, then in the case of the generalized hurst exponent:

$$K_q(\tau) \sim c(q) \tau^{qH(q)}$$

We would have that:

$$\lim_{\tau \to \infty}\frac{K_q(\tau)}{c(q) \tau^{qH(q)}} \rightarrow 1$$ ?

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1 Answer

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Yes it is.

By definition, saying $x_n \sim y_n$ means that the ratio $\frac{x_n}{y_n}\to 1$, which indicates that $x_n$ and $y_n$ have the same limit (it can be infinity) and same convergence/divergence speed.

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