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Convergence in distribution of r.v.

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#probability-theory #probability-distributions #normal-distribution #weak-convergence
70
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(Weak) Convergence of stationary distributions under tightness

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#weak-convergence #probability-limit-theorems #stationary-processes
100
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In Wasserstein, what is the relationship between $W_2 (\widehat{\mathbb{P}}_{N},\mathbb{P})$ and $W_2 (\widehat{\mathbb{P}}_{N}^{x},\mathbb{P}^{x})$?

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#probability #probability-theory #measure-theory #probability-distributions #weak-convergence
140
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Conditions for extending convergence in distribution of a subsequence to the entire sequence

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#probability-theory #convergence-divergence #weak-convergence
1.7k
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$X_n \Rightarrow X$ and $Y_n \Rightarrow c$, c a constant, implies $X_nY_n \Rightarrow Xc$

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#probability-theory #probability-distributions #weak-convergence
137
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Strong convergence of a product of weakly converging functions

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#functional-analysis #lp-spaces #weak-convergence
39
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Separating Class Limit

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#probability-theory #measure-theory #stochastic-processes #weak-convergence
44
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Convergence of a function of correlated random variables

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#convergence-divergence #asymptotics #uniform-convergence #weak-convergence #law-of-large-numbers
82
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Borel-$\sigma$-algebra on D[0,1]

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#stochastic-processes #weak-convergence #stochastic-analysis #skorohod-space
85
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Integral with parameters, limit permutation and weak convergence in $L^2$

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#functional-analysis #improper-integrals #lp-spaces #weak-convergence
135
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Weak and strong product convergence exercise

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#functional-analysis #hilbert-spaces #lp-spaces #weak-convergence
276
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Weak convergence of measure, uniform convergence of its Fourier transform

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#functional-analysis #measure-theory #weak-convergence
181
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Weak convergence of a sequence of probability measures implies integrability of the limiting probability measure

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#probability #probability-theory #measure-theory #weak-convergence #uniform-integrability
514
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If $a X_n + b Y_n$ converges in distribution for every $a \geq 0$ and $b \geq 0$, then $(X_n,Y_n)$ converges in distribution?

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#probability-theory #probability-distributions #weak-convergence
51
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Tightness for law of discrete time martingale

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#probability-theory #martingales #weak-convergence

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