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Stochastic measure diffusions as models of growth and spread

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Stochastic Spatial Processes

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1212))

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References

  • Bailey, N.T.J. (1968). Stochastic birth, death, and migration processes for spatially distributed populations. Biometrika 50, 189–198.

    Article  MathSciNet  MATH  Google Scholar 

  • Billingsley, P. (1968). Convergence of Probability Measures. New York: John Wiley.

    MATH  Google Scholar 

  • Bramson, M. and Griffeath, D. (1980). The asymptotic behaviour of a probabilistic model of tumor growth. In: Biological Growth and Spread. Mathematical Theories and Applications. W. Jäger, H. Rost, P. Tautu (eds.). Berlin: Springer, 165–172.

    Google Scholar 

  • Crow, J.F. and Kimura, M. (1970). An Introduction to Poputation Genetics Theory. New York: Harper and Row.

    MATH  Google Scholar 

  • Dawson, D.A. (1975). Stochastic evolution equations and related measure processes. J. Multivariate Anal. 5, 1–52.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawson, D.A. (1977). The critical measure diffusion process. Z. Wahrscheinlichkeitstheorie Verw. Gebiete 40, 125–145.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawson, D.A. (1978). Geostochastic calculus. Canad. J. Statist. 6, 143–168.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawson, D.A. (1980) Qualitative behavior of geostochastic systems. Stoch. Proc. Appl. 10, 1–31.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawson, D.A. and Hochberg, K. (1979). The carrying dimension of a stochastic measure diffusion. Ann. Prob. 7, 693–703.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawson, D.A. and Hochberg, K. (1982). Wandering random measures in the Fleming-Viot model. Ann. Prob. 10, 554–580.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawson, D.A. and Hochberg, K. (1983). Qualitative behavior of a selectively neutral allelic model. Theor. Popn. Biot. 23, 1–18.

    Article  MATH  Google Scholar 

  • Ethier, S.N. (1976). A class of degenerate diffusion processes occuring in population genetics theory. Comm. Pure Appl. Math., 29, 483–493.

    Article  MathSciNet  MATH  Google Scholar 

  • Feller, W. (1951). Diffusion processes in genetics. Proc. 2nd Berkeley Symp. Math. Statist. Prob., 227–246.

    Google Scholar 

  • Fleming, W.H. and Viot, M. (1979). Some measure valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28, 817–843.

    Article  MathSciNet  MATH  Google Scholar 

  • Jagers, P. (1971). Diffusion approximations of branching processes. Ann. Math. Statist. 42, 2074–2078.

    Article  MathSciNet  MATH  Google Scholar 

  • Karlin, S. and McGregor, J. (1964). On some stochastic models in genetics. In: Stochastic Models in Medicine and Biology. J. Gurland (ed.). Madison: University of Wisconsin Press, 249–279.

    Google Scholar 

  • Keiding, N. (1975). Extinction and exponential growth in random environments. Theor. Popn. Biol. 8, 49–63.

    Article  MATH  Google Scholar 

  • Keiding, N. (1976). Population growth and branching processes in random environments. Proc. 9th Int. Biometric Conf. Boston. 149–165.

    Google Scholar 

  • Kurtz, T.G. (1975). Semigroups of conditioned shifts and approximations of Markov processes. Ann. Prob. 3, 618–648.

    Article  MathSciNet  MATH  Google Scholar 

  • Kurtz, T.G. (1979). Diffusion approximations of branching processes. In: Branching Processes, Adv. Prob. 5, A. Joffe and P. Ney (eds.). New York: Marcel Dekker, 269–292.

    Google Scholar 

  • Potten, C.S. (1980). Protiferative cell populations in surface epithelia: Biological models for cell replacement. In: Biological Growth and Spread. Mathematical Theories and Applications. W. Jäger, H. Rost, P. Tautu (eds.). Berlin: Springer, 23–35.

    Google Scholar 

  • Rosenkranz, G. (1985). Stochastic measure diffusions as models of growth and spread. Preprint. Sonderforschungsbereich 123, Universität Heidelberg.

    Google Scholar 

  • Sato, K.J. (1976). Diffusion processes and a class of Markov chains related to population genetics. Osaka J. Math. 13, 631–659.

    MathSciNet  MATH  Google Scholar 

  • Schürger, K. and Tautu, P. (1976). A Markovian configuration model for carcinogenesis. In: Mathematical Models in Medicine. J. Berger, W. Bühler, R. Repges, P. Tautu (eds.). Berlin: Springer, 92–108.

    Chapter  Google Scholar 

  • Stroock, D.W. and Varadhan, S.R.S. (1979). Multidimensional Diffusion Processes. Berlin: Springer.

    MATH  Google Scholar 

  • Tautu, P. (1980). Biological interpretation of a random configuration model for carcinogenesis. In: Biological Growth and Spread. Mathematical Theories and Applications. W. Jäger, H. Rost. P. Tautu (eds.). Berlin: Springer, 196–220.

    Google Scholar 

  • Williams, T. and Bjerkness, R. (1972). Stochastic model for abnormal clone spread through epithelial basal layer. Nature 236, 19–21.

    Article  Google Scholar 

  • Wofsy, C. (1980). Behavior of limiting diffusions for density dependent branching processes. In: Biological Growth and Spread. Mathematical Theories and Applications. W. Jäger, H. Rost, P. Tautu (eds.). Berlin: Springer, 130–137.

    Google Scholar 

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Authors and Affiliations

  1. Sonderforschungsbereich 123, Universität Heidelberg, Im Neuenheimer Feld 293, 6900, Heidelberg

    Gerd Rosenkranz

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  1. Gerd Rosenkranz
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Petre Tautu

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© 1986 Springer-Verlag

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Rosenkranz, G. (1986). Stochastic measure diffusions as models of growth and spread. In: Tautu, P. (eds) Stochastic Spatial Processes. Lecture Notes in Mathematics, vol 1212. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076252

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  • DOI: https://doi.org/10.1007/BFb0076252

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16803-4

  • Online ISBN: 978-3-540-47053-3

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