For questions concerning a specific proof, asking for verification, identifying errors, suggestions for improvement, etc.

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Understanding proof of Peano's existence theorem

I'm studying the proof of Peano's existence theorem on this paper. At page 5 it is said that the problem $$\begin{cases} y(t) = y_0 & \forall t ∈ [t_0, t_0 + c/k] \\ y'(t) = f(t − c/k, y(t − ...
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Induced Markov chain - verify Markov property and another property

First, here is how we defined induced Markov chains: Suppose that $(X,E,P)$ is an irreducible Markov chain, where $X=(X_i)_{i\in\mathbb{N}_0}$, $E$ is the state space and $P=(p_{i,j})_{i,j\in E}$ is ...