Questions tagged [convergence-divergence]

Convergence and divergence of sequences and series and different modes of convergence and divergence. Also for convergence of improper integrals.

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Interpretation of "Noise" in Function Optimization

I am trying to better understand the meaning of "noise" with regards to function optimization - specifically, why "Noisy" functions are more difficult to optimize compared to "...
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Can two sequences of r.v be asymptotically equivalent?

I wanted to ask if the following notations make sense and/or are used. Convergence in distribution of a sequence $X_n$ of real random variables to the random variable $X$ is often indicated like this: ...
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$X \geq 0$, $E[X] =\infty$. What's a lower bound for speed at which sample mean $\overline X_n$ diverges toward $\infty$?
Question Let $X_1, X_2, \dots \sim F$ be an i.i.d. sequence of observations such that $X_1 \geq 0$ and $E X_1 = \infty$. Set the sample mean $\overline X_n := \frac 1n \sum_{i=1}^n X_i$. We know that \$...