REWARD PROCESSES WITH NONLINEAR REWARD FUNCTIONS

Based on a semi-Markov process J(t), t greater than or equal to 0, a r eward process Z(t), t greater than or equal to 0, is introduced where it is assumed that the reward function, rho(k, x) is nonlinear; if the reward function is linear, i.e. rho(k, x) = kx, the reward process Z( t), t greater than or equal to 0, becomes the classical one, which has been considered by many authors. An explicit formula for E(Z(t)) is g iven in terms of the moments of the sojourn time distribution at t, wh en the reward function is a polynomial.