Abstract
We give a brief review of the ergodic theory of critical branching random walk, and summarize some new work that extends this theory.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.T. Cox, On the ergodic theory of critical branching Markov chains, preprint (1991).
J.T. Cox and A. Greven, On the ergodic theory of critical branching Brownian motion in low dimensions, preprint (1991).
J.T. Cox and A. Greven, On the long term behavior of some finite particle systems, Prob. Th. Rel. Fields 85 (1990), pp. 195–237.
D.A. Dawson, R.D. Foley, K. Fleischmann, L.A. Peletier, A critical measure-valued branching process with infinite mean, Stoch. Anal. Appl. 4 (1988), pp. 117–129.
S. Ethier and T. Kurtz, “Markov Processes — Characterization and Convergence,” Wiley, New York, 1986.
R Durrett, An infinite particle system with additive interactions, Adv. Appl. Prob. 11 (1979), pp. 355–383.
T.E. Harris, Additive set-valued Markov processes, Ann. Probab 6 (1978), pp. 355–378.
R. Holley and T.M. Liggett, Generalized potlatch and smoothing, Z. Wahrsch. Verw. Gebeite 55 (1981), pp. 165–195.
O. Kallenberg, Stability of critical cluster fields, Math. Nachr. 77 (1977), pp. 7–43.
T.M. Liggett and F.L. Spitzer, Ergodic theorems for coupled random walks and other systems with locally interacting components, Z. Wahrsch. Verw. Gebeite 56 (1981), pp. 443–468.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer Science+Business Media New York
About this chapter
Cite this chapter
Cox, J.T. (1991). Some Remarks on the Theory of Critical Branching Random Walk. In: Alexander, K.S., Watkins, J.C. (eds) Spatial Stochastic Processes. Progress in Probability, vol 19. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0451-0_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0451-0_2
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6766-9
Online ISBN: 978-1-4612-0451-0
eBook Packages: Springer Book Archive