Logarithmic estimates for nonsymmetric martingale transforms

Ose[combining cedilla]kowski, Adam

Statistics & Probability Letters, 2010, vol. 80, issue 7-8, 678-682

Abstract: Let be a martingale difference sequence and be a predictable sequence taking values in [0,1]. In this paper we study the inequality and show that it holds with some universal L(K) 1/2. Furthermore, we determine the optimal value of L(K) for K>=1 and the optimal order of L(K) as K-->1/2. Related estimates for stochastic integrals are also established.

Date: 2010
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