Recent content by CHatUPenn

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    Graduate Proving: If Xt -> 0 as t -> ∞, (1/T)sum (Xt) -> 0

    T is number of terms of the summation
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    Graduate Proving: If Xt -> 0 as t -> ∞, (1/T)sum (Xt) -> 0

    How to prove If Xt goes to zero as t goes to infinite, (1/T)sum (Xt) also goes to zero ? (average of Xt) Many thanks
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    Graduate Is Martingale difference sequence strictly stationary and ergodic?

    Is Martingale difference sequence strictly stationary and ergodic? It seems to me that Martingale Difference Sequence is a special case of strictly stationary and ergodic sequences. Also, can somebody give me an example of strict stationarity without independence. Cheers
    • CHatUPenn
    • Thread
    • Difference martingale Sequence
    • Replies: 1
    • Forum: Calculus
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    Graduate Compact-valued range doesnot imply compact graph

    Quasar 987: I just edited my question. Assuming X is compact,... The statement is true even though the domain is compact. I can tell you are doing physics. I am doing economics, sin function will never cross my mind. Cheers
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    Graduate Convexity of set A = {(x,y) in R^2 | x^4+y^4 =< 1, x>=0

    I am sure it can be shown by definition, but I propose an easy way (not rigorous though) The function is (weakly) convex The lower contour set (=<1) of a convect function is convex.
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    Graduate Compact-valued range doesnot imply compact graph

    y is a correspondence of x. X is compact. Can somebody give me an example where y is compacted valued, but the graph(x,y) is not compact. A graph will be highly appreciated.