=+most one n 2 0 such that (i, i + 1 ,..., i +n) / ,. If
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=+most one n 2 0 such that (i, i + 1 ,..., i +n) €/ ,. If there is no such n, then E{ f(X,)] =0. If there is one, then E [ f(X)] = P;[(X) ...., X„)= (i ...., i + n)]f(i+ n).
and hence the only possible values of E,[f( X,)] are 0, f(i), pif(i+ 1) =f(i)A], P;P1+1f(i + 2) = f(i)A,A+ ......
Thus v(i) = f(i)A /A, . . . A, - 1 for i ≥ 1; no strategy this value. The support set is M = (0), and the hitting time To for M is finite, but E,[ f(X, )] =0.
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Related Book For
Probability And Measure Wiley Series In Probability And Mathematical Statistics
ISBN: 9788126517718
3rd Edition
Authors: Patrick Billingsley
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