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Question

Problem:

Let (X_n) be a martingale and write ∆_n = X_n - X_n-1, Suppose that bm ↑ ∞ and Σ^∞_m=1 b ^-2m E∆²m < ∞. Prove that X_n/b_n → 0 a.s.

Additional Information:

This problem is basically from Mathematics and it is about martingale calculation

Note: The solution is in handwritten format.