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Paper IPM / M / 184  


Abstract:  
Based on a semiMarkov 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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