Geodesic
Exponential rate of $L_p$-convergence of intrinsic martingales in supercritical branching random walks
Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 1-18

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Let $W_n, n\in\mathbb{N}_{0}$ be an intrinsic martingale with almost sure limit $W$ in a supercritical branching random walk. We provide criteria for the $L_p$-convergence of the series $\sum_{n\ge 0} e^{an}(W-W_n)$ for $p>1$ and $a>0$. The result may be viewed as a statement about the exponential rate of convergence of ${\mathbb E} |W-W_n|^p$ to zero.
Keywords: Supercritical branching random walk, weighted branching process, random series, Burkholder's inequality.
Mots-clés : martingale, $L_p$-convergence 
@article{THSP_2009_15_2_a0,
     author = {G. Alsmeyer and A. Iksanov and S. Polotskiy and U. R\"osler},
     title = {Exponential rate of $L_p$-convergence of intrinsic martingales in supercritical branching random walks},
     journal = {Teori\^a slu\v{c}ajnyh processov},
     pages = {1--18},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a0/}
}
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G. Alsmeyer; A. Iksanov; S. Polotskiy; U. Rösler. Exponential rate of $L_p$-convergence of intrinsic martingales in supercritical branching random walks. Teoriâ slučajnyh processov, Tome 15 (2009) no. 2, pp. 1-18. http://geodesic.mathdoc.fr/item/THSP_2009_15_2_a0/