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Limit theorem conditioning on information set

  1. Mar 12, 2010 #1
    Would anyone be able to throw some light on the convergence of
    var[x_t | F_t] , where x_t is a stochastic time-series process, and F_t is the information (it's past history) uptil time t.

    What I mean by the question is that
    var[x_t | F_t] can be regarded as a function of F_t
    say, g(F_t)

    Now, does
    1/T*g(F_t) ----> converge in probability (a sort of Weak Law of Large Numbers) to its expectation (over the distribution of F_t)?
    (possibly under some assumptions on the dependence of F_t through time ?)

    Thanks for any help
  2. jcsd
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