Stochastic process modeling point hopping

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Let $(X_n)_n$ be a stochastic process (with application regards $X_n$ as a distance between two points, hence those squares) with the next property



$mathbbE(X_n^2 | X_n-1) = X_n-1^2 - X_n-1 - 2$ and suppose $X_0$ is some (large enough) positive constant, so we do not have to deal with possibly negative values.



Is it true, that $mathbbE(X_n | X_n-1) = X_n-1 - frac12$ ?



Can something be said about $mathbbE(X_n | X_n-1)$ at all?




stochastic-processes conditional-expectation




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    up vote
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    down vote

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    Let $(X_n)_n$ be a stochastic process (with application regards $X_n$ as a distance between two points, hence those squares) with the next property



    $mathbbE(X_n^2 | X_n-1) = X_n-1^2 - X_n-1 - 2$ and suppose $X_0$ is some (large enough) positive constant, so we do not have to deal with possibly negative values.



    Is it true, that $mathbbE(X_n | X_n-1) = X_n-1 - frac12$ ?



    Can something be said about $mathbbE(X_n | X_n-1)$ at all?




    stochastic-processes conditional-expectation




    share|cite|improve this question





















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      Let $(X_n)_n$ be a stochastic process (with application regards $X_n$ as a distance between two points, hence those squares) with the next property



      $mathbbE(X_n^2 | X_n-1) = X_n-1^2 - X_n-1 - 2$ and suppose $X_0$ is some (large enough) positive constant, so we do not have to deal with possibly negative values.



      Is it true, that $mathbbE(X_n | X_n-1) = X_n-1 - frac12$ ?



      Can something be said about $mathbbE(X_n | X_n-1)$ at all?




      stochastic-processes conditional-expectation




      share|cite|improve this question











      Let $(X_n)_n$ be a stochastic process (with application regards $X_n$ as a distance between two points, hence those squares) with the next property



      $mathbbE(X_n^2 | X_n-1) = X_n-1^2 - X_n-1 - 2$ and suppose $X_0$ is some (large enough) positive constant, so we do not have to deal with possibly negative values.



      Is it true, that $mathbbE(X_n | X_n-1) = X_n-1 - frac12$ ?



      Can something be said about $mathbbE(X_n | X_n-1)$ at all?





      stochastic-processes conditional-expectation





      share|cite|improve this question










      share|cite|improve this question




      share|cite|improve this question









      asked Jul 26 at 19:48









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