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3 First show by induction that frx increases monotonically with x Thus if v
20 Replace Min by Max in Ex 19 for the functional equations
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3-stage analogously to Eq analytical assume Bayesian probabilities boundary chapter choose computational computationally computer storage consider constant stock level constraints convex function corresponding defined density function determine deterministic discrete search discussion distribution dynamic programming example expected cost Fairplay fi(x final assets finite fN(x follows from Eq fr(x fr+i(x functional equations gambler's ruin gives grid Hence increases induction infinite-stage process initial state x0 intuitively inventory investment l)-stage Lagrange multipliers mathematical maximize methods minimize module monotonically multi-stage decision processes notation Note obtained optimal decisions optimal policy parameters possible posteriori principle of optimality priori problem process starting random variable random walk reader Repeat Ex respectively right-hand side sequential sequential analysis Similarly simulation solution solve stage stochastic stochastic processes successive approximations Suppose tables time-period tions TV-stage process v,+i values x,+i x.+i zero