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References
Biggins, J.D.: The asymptotic shape of the branching random walk. Advances in Appl. Probability 10, 62–84 (1978)
Blumenthal, R.M., Getoor, R.K.: Markov Processes and Potential Theory. New York: Academic Press 1968
Hammersley, J.M.: Generalization of the fundamental theorem on subadditive functions. Proc. Cambridge Philos. Soc. 58, 235–238 (1962)
Hammersley, J.M.: Postulates for subadditive processes. Ann. Probability 2, 652–680 (1974)
Harris, T.E.: Contact interactions on a lattice. Ann. Probability 2, 969–988 (1974)
Holley, R.: Markovian interaction processes with finite range interactions. Ann. Math. Statist. 43, 1961–1967 (1972)
Kesten, H.: Contribution to the discussion in [8], p. 903
Kingman, J.F.C.: Subadditive ergodic theory. Ann. Probability 1, 883–909 (1973)
Liggett, T. M.: Existence theorems for infinite particle systems. Trans. Amer. Math. Soc. 115, 471–481 (1972)
Mollison, D.: Conjecture on the spread of infection in two dimensions disproved. Nature 240, 467–468 (1972)
Mollison, D.: Markovian contact processes. Advances in Appl. Probability 10, 85–108 (1978)
Richardson, D.: Random growth in a tessellation. Proc. Cambridge Philos. Soc. 74, 515–528 (1973)
Schürger, K., Tautu, P.: Markov configuration processes on a lattice. Revue Roumaine Math. Pures Appl. 21, 233–244 (1976)
Schürger, K., Tautu, P.: A Markovian configuration model for carcinogenesis. In: Mathematical Models in Medicine (Berger, J., Bühler, W., Repges, R., Tautu, P., eds.). Lecture Notes in Biomathematics 11, 92–108. Berlin-Heidelberg-New York: Springer 1976
Williams, T., Bjerknes, R.: Stochastic model for abnormal clone spread through epithelial basal layer. Nature 236, 19–21 (1969)
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Schürger, K. On the asymptotic geometrical behaviour of a class of contact interaction processes with a monotone infection rate. Z. Wahrscheinlichkeitstheorie verw Gebiete 48, 35–48 (1979). https://doi.org/10.1007/BF00534880
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DOI: https://doi.org/10.1007/BF00534880