# Questions tagged [convergence]

Convergence generally means that a sequence of a certain sample quantity approaches a constant as the sample size tends to infinity. Convergence is also a property of an iterative algorithm to stabilize on some aim value.

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### What does weak convergence mean for a stochastic process?

I am reading a paper in which stochastical processes $\{\mathcal{H}_T(u)\}_{u\in[0,1]}$ and $\{\mathcal{H}(u)\}_{u\in[0,1]}$ on [0,1] with $u$ as a time-index occur. There is a theorem which states ...
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### Logit/Probit: algorithm did not converge and sampling weights

I am running a logit regression in R. I get a warning which signals the missing algorithm convergence. My experience suggests that the problem may be due to the number of dummies in the model and/or ...
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### A dynamical systems view of the Central Limit Theorem?

(Originally posted on MSE.) I have seen many heuristic discussions of the classical central limit theorem speak of the normal distribution (or any of the stable distributions) as an "attractor" in ...
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### Convergence of distribution

This is from Probability and Measure by Billingsley, 3rd Edition. 27.21 (p. 370) Let $X_1, X_2,...$ be independent and identically distributed, and suppose that the distribution common to the $X_n$ ...
Let's say you have infinitely many i.i.d. Bernouilli variables $X_1, X_2, \cdots$ of parameter $p=\frac{1}{2}$. For instance, the binary digits of a random number. Let $S_n = X_1 + \cdots X_n$. The ...