Exercises and Problems in Linear Algebra (John M Erdman)
... verify that {Yn,n ? 0} inherits the submartingale property of {Xn,n ? 0}. Since ?n+1 > n, we have. Yn. = Yn??1 + n. X i=1. (Yn??i ? Yn??i ) + n. X i=1. Yn??i+1 ... 
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