Abstract
We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in \(\mathbb{L}^{p}\) for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am. Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of \(\mathbb{L}^{p}\) -norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular Markov chain are given.
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Rio, E. Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions. J Theor Probab 22, 146–163 (2009). https://doi.org/10.1007/s10959-008-0155-9
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DOI: https://doi.org/10.1007/s10959-008-0155-9