# Tagged Questions

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-...

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### Equality of random variables measurable w.r.t. different sigma-algebras

I'm stuck trying to prove the following statement: Let $\tau$ be a non-negative random variable on the probability space $(\Omega, \mathcal{F}, \mathbb{P})$. We'll consider the following ...
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### powers of the transition matrix for a subshift of finite type

Is there a relation between powers of the transition matrix for a subshift of finite type and iterations of the (forward) subshift? It is very nice to understand the transition matrix via a graph and ...
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### Square Integrable Martingales and the Unit Process

Let $X_t$ be a continuous square-integrable martingale. Then it is true (I think, please correct me if I am wrong) that: $$\forall t \in [0,\infty), \quad \int_0^t 1_{[0,t]}(s) dX_s = X_t - X_0$$ So ...
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### Does it follow that $\mu$ is a measure? [duplicate]

Suppose $\mu_n$ is a sequence of measures on $(X, \mathcal{A})$ such that $\mu_n(X) = 1$ for all $n$ and $\mu_n(A)$ converges as $n \to \infty$ for each $A \in \mathcal{A}$. Cal the limit $\mu(A)$. ...
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### Representation of Matrix Calculations - Column Mean Subtract From Each Row

Suppose I have a matrix that looks like this: $$X = \begin{bmatrix}1 & 1 & 1 & 1 \\ 1 & 0 & 0 & 0 \\ 1 & 1 & 0 & 0 \\ 1 & 1 & 1 & 0\end{bmatrix}$$ The ...