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1 results

  • On two classes of interacting stochastic processes arising in cancer modeling

  • Robert Bartoszyński, Prem S. Puri
  • Journal:
    Advances in Applied Probability / Volume 15 / Issue 4 / December 1983
    Published online by Cambridge University Press:
    01 July 2016, pp. 695-712
    Print publication:
    December 1983

  • The processes X and Y are said to interact if the laws governing the changes of either of them at time t depend on the values of the other process at times up to t. For bivariate interacting Markov processes, their limiting behavior is analysed by means of an approximation suggested by Fuhrmann, consisting of discretizing time, and assuming that in each time interval the processes develop independently, according to the laws obtained by fixing the value of the other process at its level attained at the beginning of the interval.

    In this way the conditions for almost sure extinction, escape to ∞ with positive probability, etc., are obtained (by using the martingale convergence theorem) for state-dependent branching processes studied by Roi, and for bivariate processes with one component piecewise determined.