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An Extension to the Tangent Sequence Martingale Inequality

Stephen Montgomery-Smith, Shih-Chi Shen

math.PRarXiv:math/0107120

Abstract

For each 1 < p < infinity, there exists a positive constant cp, depending only on p, such that the following holds. Let (dk), (ek) be real-valued martingale difference sequences. If for for all bounded nonnegative predictable sequences (sk) and all positive integers k we have E[sk vee |ek|] le E[sk vee |dk|] then for all positive integers n we have || sumk=1n ek ||p le cp || Σk=1n dk ||p .

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