About distribution convergence consequence [on hold]Convergence of marginal distribution in the case of convergence in distributionA small question about convergence in distributionWeak version Fatou lemmaJoint convergence in distribution$X_n stackreldtoX$, $Y_n stackreldto c implies X_n+Y_n stackreldto X+c$About convergence in probabilityConvergence in probability implies convergence in distribution of random variablesProbability distribution and convergence almost surelyIndependent random variables, equivalent in distribution, almost sure convergenceConvergence in distribution implies convergence of $L^p$ norms under additional assumption
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About distribution convergence consequence [on hold]
Convergence of marginal distribution in the case of convergence in distributionA small question about convergence in distributionWeak version Fatou lemmaJoint convergence in distribution$X_n stackreldtoX$, $Y_n stackreldto c implies X_n+Y_n stackreldto X+c$About convergence in probabilityConvergence in probability implies convergence in distribution of random variablesProbability distribution and convergence almost surelyIndependent random variables, equivalent in distribution, almost sure convergenceConvergence in distribution implies convergence of $L^p$ norms under additional assumption
$begingroup$
Assume that $X_n rightarrow X$ in distribution. Are there $Y_n$ and $Y$ such that $Y_n rightarrow Y$ almost surely and their distribution functions satisfy $F_X_n=F_Y_n$, $F_X=F_Y$?
probability-theory convergence random-variables
edited 2 days ago
Mars Plastic
1,294121
asked 2 days ago
user157895564user157895564
836
$endgroup$
put on hold as unclear what you're asking by Theoretical Economist, Davide Giraudo, Lee David Chung Lin, Shailesh, Eevee Trainer 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
Assume that $X_n rightarrow X$ in distribution. Are there $Y_n$ and $Y$ such that $Y_n rightarrow Y$ almost surely and their distribution functions satisfy $F_X_n=F_Y_n$, $F_X=F_Y$?
probability-theory convergence random-variables
edited 2 days ago
Mars Plastic
1,294121
asked 2 days ago
user157895564user157895564
836
$endgroup$
put on hold as unclear what you're asking by Theoretical Economist, Davide Giraudo, Lee David Chung Lin, Shailesh, Eevee Trainer 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
Assume that $X_n rightarrow X$ in distribution. Are there $Y_n$ and $Y$ such that $Y_n rightarrow Y$ almost surely and their distribution functions satisfy $F_X_n=F_Y_n$, $F_X=F_Y$?
probability-theory convergence random-variables
edited 2 days ago
Mars Plastic
1,294121
asked 2 days ago
user157895564user157895564
836
$endgroup$
Assume that $X_n rightarrow X$ in distribution. Are there $Y_n$ and $Y$ such that $Y_n rightarrow Y$ almost surely and their distribution functions satisfy $F_X_n=F_Y_n$, $F_X=F_Y$?
probability-theory convergence random-variables
probability-theory convergence random-variables
edited 2 days ago
Mars Plastic
1,294121
asked 2 days ago
user157895564user157895564
836
edited 2 days ago
Mars Plastic
1,294121
asked 2 days ago
user157895564user157895564
836
edited 2 days ago
Mars Plastic
1,294121
edited 2 days ago
Mars Plastic
1,294121
edited 2 days ago
Mars Plastic
1,294121
1,294121
asked 2 days ago
user157895564user157895564
836
asked 2 days ago
user157895564user157895564
836
asked 2 days ago
user157895564user157895564
836
836
put on hold as unclear what you're asking by Theoretical Economist, Davide Giraudo, Lee David Chung Lin, Shailesh, Eevee Trainer 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as unclear what you're asking by Theoretical Economist, Davide Giraudo, Lee David Chung Lin, Shailesh, Eevee Trainer 2 days ago
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.
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1 Answer
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$begingroup$
Yes. This is called the Skorokhod representation theorem. Note that, using the notation from wikipedia, separability of the support of $mu_infty$ is always given when the metric space $S$ is already separable - as is the case for $S=Bbb R^N$.
answered 2 days ago
Mars PlasticMars Plastic
1,294121
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Yes. This is called the Skorokhod representation theorem. Note that, using the notation from wikipedia, separability of the support of $mu_infty$ is always given when the metric space $S$ is already separable - as is the case for $S=Bbb R^N$.
answered 2 days ago
Mars PlasticMars Plastic
1,294121
$endgroup$
add a comment |
$begingroup$
Yes. This is called the Skorokhod representation theorem. Note that, using the notation from wikipedia, separability of the support of $mu_infty$ is always given when the metric space $S$ is already separable - as is the case for $S=Bbb R^N$.
answered 2 days ago
Mars PlasticMars Plastic
1,294121
$endgroup$
add a comment |
$begingroup$
Yes. This is called the Skorokhod representation theorem. Note that, using the notation from wikipedia, separability of the support of $mu_infty$ is always given when the metric space $S$ is already separable - as is the case for $S=Bbb R^N$.
answered 2 days ago
Mars PlasticMars Plastic
1,294121
$endgroup$
Yes. This is called the Skorokhod representation theorem. Note that, using the notation from wikipedia, separability of the support of $mu_infty$ is always given when the metric space $S$ is already separable - as is the case for $S=Bbb R^N$.
answered 2 days ago
Mars PlasticMars Plastic
1,294121
edited 2 days ago
answered 2 days ago
Mars PlasticMars Plastic
1,294121
answered 2 days ago
Mars PlasticMars Plastic
1,294121
answered 2 days ago
Mars PlasticMars Plastic
1,294121
1,294121
add a comment |
add a comment |
