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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, $\rho(k,x)$ is nonlinear; if the reward
function is linear, i.e. $\rho(k,x)=kx$, the reward process
$Z(t)$, $t\geqq 0$, becomes the classical one, which has been
considered by many authors. An explicit formula for {\bf
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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