An Extension to the Tangent Sequence Martingale Inequality

Stephen Montgomery-Smith; Shih-Chi Shen

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An Extension to the Tangent Sequence Martingale Inequality

Stephen Montgomery-Smith·Shih-Chi Shen

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Abstract

For each 1 < p < infinity, there exists a positive constant c_p, depending only on p, such that the following holds. Let (d_k), (e_k) be real-valued martingale difference sequences. If for for all bounded nonnegative predictable sequences (s_k) and all positive integers k we have E[s_k vee |e_k|] le E[s_k vee |d_k|] then for all positive integers n we have || sum_{k=1}^n e_k ||_p le c_p || \sum_{k=1}^n d_k ||_p .

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Stephen Montgomery-Smith, Shih-Chi Shen. 2001-07-23. An Extension to the Tangent Sequence Martingale Inequality. https://arxiv.org/abs/math/0107120

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