Multistage Stochastic Programming via Autoregressive Sequences

Multistage stochastic programming problems belong to optimization problems depending on a probability measure. Usually, the operator of mathematical expectation appears in an objective function and, moreover, constraints set can depend on the probability measure also. The multistage stochastic programming problems correspond to applications (with an unneglected random element) that can be reasonably considered with respect to some finite "discrete" (say (1 ) 2 M M    ) time interval and simultaneously there exists a possibility to decompose them with respect to the individual time points. Moreover, a decision, at every individual time point say k can depend only on the random elements realizations and the decisions to the time point 1 k  (we say that it must be nonanticipative).