Exponential rate of L_p-convergence of intrinsic martingales in supercritical branching random walks

Details Exponential rate of L_p-convergence of intrinsic martingales in supercritical branching random walks Exponential rate of L_p-convergence of intrinsic martingales in supercritical branching random walks

2009-03-23

arxiv.org/abs/0903.3935v1

Mathematics

Probability

Scientific paper

Let $W_n, n\in\mn_{0}$ 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 $\me |W-W_n|^p$ to zero.

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