Abstract
Differential equations are derived for a class of interacting lattice particle processes first introduced in [11]. When there is one type of particle, the equations are in terms of the moments of boundary counts and particle counts. When there are two types of particles, the equations are in terms of the moments of certain neighbourhood statistics as well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Braun, W. J., Kulperger, R. J.: Coupling Results for Family of Interacting Lattice Process. Technical Report, University of Western Ontario (1991)
Braun, W. J., Kulperger, R. J., Lockman, T.: Statistical Identification of a One Type Interacting Particle System on a Lattice. Technical Report, University of Western Ontario (1991)
Chover, J., King, J. H.: The Early Growth of Cancer. J. Math. Biol. 21, 329–346 (1985)
Clark, W. H., Elder, D. E., Dupont, G., Martin, N. E., Greene, M. H., Van Horn, M.: A Study of Tumor Progression: The Precursor Lesions of Superficial Spreading and Nodular Melanoma. Hum. Pathol. 15, 1147–1165 (1984)
Grimmett, G. R., Stirzaker, D. R.: Introduction to Probability and Random Processes. Oxford: Oxford University Press 1985
Hammersley, J. M. First-Passage Percolation. J. Roy. Statist. Soc., B, 491–496 (1966)
Karlin, S., Taylor, H. M.: A First Course in Stochastic Processes. New York: Academic Press 1975
Liggett, T.: Interacting Particle Systems. New York: Springer 1985
Rothinger, B., Tautu, P.: On the Genealogy of Large Cell Populations. (Stochastic) In: Modeling in Biology, pp. 166–235. Singapore: World Scientific 1990
Rudin, W.: Principles of Mathematical Analysis, 3rd ed. New York: McGraw-Hill 1976
Schuger, K., Tautu, P.: A Markovian Configuration Model for Carcinogenesis. (Lect. Notes Biomath., vol. 11, pp. 92–108) Berlin Heidelberg New York: Springer 1976
Thompson, J. R., Brown, B. W. (eds.): Cancer Modeling. New York: Marcel Dekker 1987
Author information
Authors and Affiliations
Additional information
This work has been supported by grants from the Natural Sciences and Engineering Research Council of Canada. WJB also acknowledges support of an Ontario Graduate Scholarship
Rights and permissions
About this article
Cite this article
Braun, W.J., Kulperger, R.J. Differential equations for moments of an interacting particle process on a lattice. J. Math. Biol. 31, 199–214 (1993). https://doi.org/10.1007/BF00171227
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00171227