# Questions tagged [limits-and-convergence]

Convergence of series, sequences and functions and different modes of convergence.

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### Solve divergent iteration to a certain number of decimal places [closed]

I have a quantity X which I have to take a percentage of, but then it adds to the quantity and the percentage has to be taken of the new result. This ends up in the divergent equation: ...
1 vote
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### Proof of convergence of sets

Consider the following sets: \begin{align} &A(y) \equiv \Bigl\{ x\in X: \Pr\biggl(\lim_{n \to \infty}d\bigl(p_n(y), [\ell(x,y), u(x,y) ] \bigr)= 0\biggr)=1 \Bigr\},\\ & A_n(y) \equiv \Bigl\{...
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### Supremum or upper bound of bivariate function involving logarithms and combinatorial coefficients or the gamma function over a region of the integers

This is a repost from MSE because I got no answers there. I have been trying to find the supremum of this bivariate function over a specific region. However, the expressions that I get are horrible. I ...
• 573
1 vote
Suppose we have a discrete time (not necessarily stationary) Markov chain $X=(X_0,X_1,X_2,\dots)$ on $(\Omega, F)$. We assume $X$ is Harris ergodic with an invariant distribution. Suppose we have a ...