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Paper   IPM / M / 184
School of Mathematics
  Title:   Reward processes with nonlinear reward functions
  Author(s):  A. R. Soltani
  Status:   Published
  Journal: J. Appl. Probab.
  Vol.:  33
  Year:  1996
  Pages:   1011-1017
  Supported by:  IPM
  Abstract:
Based on a semi-Markov process J(t), t\geqq 0, a reward process Z(t), t\geqq 0, is introduced where it is assumed that the reward function, ρ(k,x) is nonlinear; if the reward function is linear, i.e. ρ(k,x)=kx, the reward process Z(t), t\geqq 0, becomes the classical one, which has been considered by many authors. An explicit formula for E(Z(t)) is given in terms of the moments of the sojourn time distribution at t, when the reward function is a polynomial.

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