Abstract
We describe a class of multilevel multitype branching particle systems and indicate how it can be applied to model a dynamical information system.
AMS(MOS) subject classifications. Primary 60K35, Secondary 68B15.
Articefootnote
Supported partially by the NSERC.
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
Preview
Unable to display preview. Download preview PDF.
References
References Athreya, K.B. and Ney, P.E. (1977). Branching Processes. Springer-Verlag, BerlinHeidelberg-New York.
Bhattacharya, Rabi N. and Waymire, Edward C.(1990). Stochastic processes with applications. Wiley, New York.
Dawson, D. and Hochberg, K. (1991). A multilevel branching model. Adv. Appl. Prob., 23, 701–715.
D.A. Dawson (1993). Measure-valued Markov Processes in Ecole d’Eté de Probabilités de Saint-Flour XXI, Lect. Notes in Math. 1541, 1–260, Springer-Verlag.
Dawson, D.A., Hochberg, K.J. and V. Vinogradov (1994). On path properties of super-2 processes I. in Measure-Valued Processes, Stochastic Partial Differential Equations, and Interacting Systems, ed. D.A. Dawson, 69–82, CRM-AMS.
Dawson, D.A., Hochberg, K.J. and V. Vinogradov (1994). On path properties of super-2 processes II. in M. Pinsky, ed., Proceedings of the 1993 AMS Summer Res. Institute Vol. 57, 385–404, Amer. Math. Soc.
Dawson, D.A., Hochberg, K.J. and Wu, Y. (1990). Multilevel branching systems. White Noise Analysis, World Scientific Publ.
Dawson, D.A. and Ivanoff, B.G. (1978). Branching diffusions and random measures. In Branching Processes, ed. A. Joffe and P. Ney, 61–104, Dekker, New York.
D.A. Dawson and Y. Wu (1994) Simulation of hierarchically structured information systems. preprint.
L.G. Gorostiza (1994) Asymptotic fluctuations and critical dimension for a two-level branching system, preprint.
Gorostiza, L.G., Hochberg, K.J. and Wakolbinger, A.. Persistence of a critical super-2 process. J. Appl. Prob., in press.
Harris, T.E.(1963). The Theory of Branching Processes. Springer, Berlin.
K.J. Hochberg (1993) Hierarchically structured branching populations with spatial motion, Rocky Mountain J. Math., to appear.
E.A. Perkins (1992). Measure-valued branching diffusions with spatial interactions, Prob. Theor. Rel. Fields 94, 189–245.
Wu, Y. (1991). Dynamic particle systems and multilevel measure branching processes, Ph.D. thesis. Carleton University.
Wu, Y. (1993). A multilevel birth-death particle system and its continuous diffusion. Adv. Appl. Prob., Vol. 25, No. 3, 549–569.
Wu, Y. (1993). Multilevel particle systems and measure-valued processes. Preprint.
Wu, Y. (1994). Asymptotic behavior of the two level measure branching process. Ann. of Prob., 22, No. 2, to appear.
Y. Wu (1994) A three level particle system and existence of general multilevel measure-valued processes in “Measure-valued Processes, Stochastic Partial Differential Equations, and Interacting Systems” CRM Proceedin gs and Lecture Notes 5, 233–241, Amer. Math. Soc.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this chapter
Cite this chapter
Dawson, D.A., Wu, Y. (1997). Multilevel Multitype Branching Models of an Information System. In: Athreya, K.B., Jagers, P. (eds) Classical and Modern Branching Processes. The IMA Volumes in Mathematics and its Applications, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1862-3_5
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1862-3_5
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-7315-8
Online ISBN: 978-1-4612-1862-3
eBook Packages: Springer Book Archive