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A Note on the Structure of a Stochastic Model Considered by V. M. Dandekar

Part of the Biomathematics book series (BIOMATHEMATICS, volume 6)

Abstract

Mr. Dandekar starts with the stochastic process x0, x1 x2,…, ad inf. which may be characterised by the following defining postulates:
  • π1: Each x i can take only the two values 0 (= failure) and 1 (= success) and the probability that x0 = 1 is p.

  • π2: For any m (or less) consecutive x i ’s at most one can be 1.

  • π3: If any m−1 (or more) consecutive x i ’s are known to be zeros then the next x i is 1 with probability p.

  • π3: If x0 = 0 then the conditional stochastic process x1, x2,… is the same as the original process x0, x1, x2,….

Let P n = P(x n = 1), n = 0, 1, 2,… (P0 = p, q = 1−p) and let φ(t) be the generating function \(\sum\limits_0^\infty {P_n t^n } .\)

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Copyright information

© Springer-Verlag Berlin · Heidelberg 1977

Authors and Affiliations

  • D. Basu

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