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













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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







share|cite|improve this question











$endgroup$



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.






















    0












    $begingroup$


    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







    share|cite|improve this question











    $endgroup$



    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.




















      0












      0








      0





      $begingroup$


      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







      share|cite|improve this question











      $endgroup$




      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






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited 2 days ago









      Mars Plastic

      1,294121




      1,294121










      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.






















          1 Answer
          1






          active

          oldest

          votes


















          1












          $begingroup$

          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 $S=Bbb R^N$.






          share|cite|improve this answer











          $endgroup$



















            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            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 $S=Bbb R^N$.






            share|cite|improve this answer











            $endgroup$

















              1












              $begingroup$

              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 $S=Bbb R^N$.






              share|cite|improve this answer











              $endgroup$















                1












                1








                1





                $begingroup$

                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 $S=Bbb R^N$.






                share|cite|improve this answer











                $endgroup$



                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 $S=Bbb R^N$.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited 2 days ago

























                answered 2 days ago









                Mars PlasticMars Plastic

                1,294121




                1,294121













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