Can an arbitrary random vector be approximated by a normal random vector?Convergence in distribution of Gaussian processesA sequence of Gaussian random vectors converges to a Gaussian random vectorA convergent sequence of normal random variablesIs the permutation of a Gaussian random vector still a Gaussian random vector?Reference request: weak-star convergence plus convergence of normsConvergence of vector of sum of random variablesDistribution of a general linear mapping of a random vectorDoes there exist a mutivariate inverse?Calculating the covariance of a given random vector in the unit squareFactorization of Square-integrable random-variables and Generalized Inverses

Is this version of a gravity generator feasible?

Why didn't Theresa May consult with Parliament before negotiating a deal with the EU?

Risk of infection at the gym?

What is the difference between "behavior" and "behaviour"?

You cannot touch me, but I can touch you, who am I?

Is the destination of a commercial flight important for the pilot?

Do sorcerers' subtle spells require a skill check to be unseen?

System.debug(JSON.Serialize(o)) Not longer shows full string

Two monoidal structures and copowering

Closest Prime Number

Are student evaluations of teaching assistants read by others in the faculty?

Trouble understanding the speech of overseas colleagues

Term for the "extreme-extension" version of a straw man fallacy?

How to write papers efficiently when English isn't my first language?

What does "I’d sit this one out, Cap," imply or mean in the context?

How easy is it to start Magic from scratch?

Purchasing a ticket for someone else in another country?

Is a stroke of luck acceptable after a series of unfavorable events?

What is the intuitive meaning of having a linear relationship between the logs of two variables?

Is expanding the research of a group into machine learning as a PhD student risky?

A particular customize with green line and letters for subfloat

Was Spock the First Vulcan in Starfleet?

Balance Issues for a Custom Sorcerer Variant

Increase performance creating Mandelbrot set in python



Can an arbitrary random vector be approximated by a normal random vector?


Convergence in distribution of Gaussian processesA sequence of Gaussian random vectors converges to a Gaussian random vectorA convergent sequence of normal random variablesIs the permutation of a Gaussian random vector still a Gaussian random vector?Reference request: weak-star convergence plus convergence of normsConvergence of vector of sum of random variablesDistribution of a general linear mapping of a random vectorDoes there exist a mutivariate inverse?Calculating the covariance of a given random vector in the unit squareFactorization of Square-integrable random-variables and Generalized Inverses













0












$begingroup$


Let $X$ be an $n$-dimensional gaussian random vector, and $Y$ be an $n$-dimensional random vector such that $det(cov(X))neq 0$ and $det (cov(Y))neq 0$.



Then, does there exists a sequence of invertible $C^1$ functions $f_k$ such that $f_kcirc X Rightarrow Y$ (weak convergence)?



Is there any reference related to this kind of problem?










share|cite|improve this question









$endgroup$
















    0












    $begingroup$


    Let $X$ be an $n$-dimensional gaussian random vector, and $Y$ be an $n$-dimensional random vector such that $det(cov(X))neq 0$ and $det (cov(Y))neq 0$.



    Then, does there exists a sequence of invertible $C^1$ functions $f_k$ such that $f_kcirc X Rightarrow Y$ (weak convergence)?



    Is there any reference related to this kind of problem?










    share|cite|improve this question









    $endgroup$














      0












      0








      0


      1



      $begingroup$


      Let $X$ be an $n$-dimensional gaussian random vector, and $Y$ be an $n$-dimensional random vector such that $det(cov(X))neq 0$ and $det (cov(Y))neq 0$.



      Then, does there exists a sequence of invertible $C^1$ functions $f_k$ such that $f_kcirc X Rightarrow Y$ (weak convergence)?



      Is there any reference related to this kind of problem?










      share|cite|improve this question









      $endgroup$




      Let $X$ be an $n$-dimensional gaussian random vector, and $Y$ be an $n$-dimensional random vector such that $det(cov(X))neq 0$ and $det (cov(Y))neq 0$.



      Then, does there exists a sequence of invertible $C^1$ functions $f_k$ such that $f_kcirc X Rightarrow Y$ (weak convergence)?



      Is there any reference related to this kind of problem?







      probability-theory probability-distributions reference-request






      share|cite|improve this question













      share|cite|improve this question











      share|cite|improve this question




      share|cite|improve this question










      asked Mar 17 at 20:42









      RubertosRubertos

      5,7642825




      5,7642825




















          0






          active

          oldest

          votes











          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3152053%2fcan-an-arbitrary-random-vector-be-approximated-by-a-normal-random-vector%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















          draft saved

          draft discarded
















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid


          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.

          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3152053%2fcan-an-arbitrary-random-vector-be-approximated-by-a-normal-random-vector%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          Moe incest case Sentencing See also References Navigation menu"'Australian Josef Fritzl' fathered four children by daughter""Small town recoils in horror at 'Australian Fritzl' incest case""Victorian rape allegations echo Fritzl case - Just In (Australian Broadcasting Corporation)""Incest father jailed for 22 years""'Australian Fritzl' sentenced to 22 years in prison for abusing daughter for three decades""RSJ v The Queen"

          Who is our nearest planetary neighbor, on average?Santa Claus flies to the South PoleSeven Spheres of Unequal Mass, a weighing problem with a twistDescribe a large integerFast Mental Calculation of $7.5^7$Math in Space (without the help of celebrities)Find the value of $bigstar$: Puzzle 8 - InequalityWho drinks beer while running anyway?A Crucial DeliveryRanking And AverageHow long will my money last at roulette?

          Daza language Contents Vocabulary Phonology References External links Navigation menudaza1242Daza"Dazaga"eeee178086576