Konrad Kolesko

Convergence of complex martingales in supercritical multi-type general branching processes in bold italic upper L Superscript bold italic q L q $\boldsymbol{L}^{\boldsymbol{q}}$ for 1 less than bold italic q less than or equals 2 1 < q ≤ 2 $1 \lt \boldsymbol{q} \leq 2$

Abstract Nerman’s martingale plays a central role in the law of large numbers for both single- and multi-type supercritical general branching processes. There are further, complex-valued Nerman-type martingales in the single-type process that figure in the finer fluctuations of t...