Geodesic
Conditional $L^1$-Convergence for the Martingale of a Critical Branching Process in Random Environment
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 195-206

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For a critical branching process $(Z_n)$ in a random environment $(\xi _n)$, a sufficient condition is given for the corresponding martingale ${Z_n}/{e^{S_n}}$ to converge in $L^1$ or to degenerate under $\mathbb P^+$, the probability under which the associated random walk is conditioned to stay nonnegative.
Keywords: branching process, random environment, multitype branching processes, change of measure
Mots-clés : martingale convergence. 
@article{TM_2022_316_a12,
     author = {Wenming Hong and Shengli Liang and Xiaoyue Zhang},
     title = {Conditional $L^1${-Convergence} for the {Martingale} of a {Critical} {Branching} {Process} in {Random} {Environment}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {195--206},
     publisher = {mathdoc},
     volume = {316},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_316_a12/}
}
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Wenming Hong; Shengli Liang; Xiaoyue Zhang. Conditional $L^1$-Convergence for the Martingale of a Critical Branching Process in Random Environment. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 195-206. http://geodesic.mathdoc.fr/item/TM_2022_316_a12/