Abstract
We will remain in the setting of the Asmussen–Hering class of BMPs, i.e., assuming (G2), and insist throughout this chapter that we are in the critical setting, that is, \(\lambda _*=0\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S.D. Durham, Limit theorems for a general critical branching process. J. Appl. Probab. 8(1), 1–16 (1971)
S.C. Harris, E. Horton, A.E. Kyprianou, M. Wang, Yaglom limit for critical neutron transport. Preprint (2021)
A.N. Kolmogorov, Zur lösung einer biologischen aufgabe. Comm. Math. Mech. Chebyshev Univ. Tomsk. 2, 1–12 (1938)
T. Mori, Neutron transport process on bounded homogeneous domain. Proc. Japan Acad. 46(9), 944–948 (1970)
E. Powell, An invariance principle for branching diffusions in bounded domains. Probab. Theory Related Fields 173(3–4), 999–1062 (2019)
Y-X. Ren, R. Song, Z. Sun, Spine decompositions and limit theorems for a class of critical superprocesses. Acta Appl. Math. 165, 91–131 (2020)
A.M. Yaglom, Certain limit theorems of the theory of branching random processes. Doklady Akad. Nauk SSSR (N.S.) 56, 795–798 (1947)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Horton, E., Kyprianou, A.E. (2023). Survival at Criticality. In: Stochastic Neutron Transport . Probability and Its Applications. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-39546-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-031-39546-8_10
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-031-39545-1
Online ISBN: 978-3-031-39546-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)