Geodesic
On the local limit theorem for critical Galton--Watson process
Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 457-479

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The proof of the local limit theorem for a critical Galton–Watson process is given under minimal moment restrictions, i.e., under the condition that there exists the second moment of the number of direct offspring of one particle.
Keywords: Galton–Watson process, Bellman–Harris process, concentration function, local theorem, bilinear generating function. 
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     title = {On the local limit theorem for critical {Galton--Watson} process},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     language = {ru},
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S. V. Nagaev; V. I. Vakhtel'. On the local limit theorem for critical Galton--Watson process. Teoriâ veroâtnostej i ee primeneniâ, Tome 50 (2005) no. 3, pp. 457-479. http://geodesic.mathdoc.fr/item/TVP_2005_50_3_a2/