Abstract
This chapter covers technical tools, that will be used throughout the book, on how to handle information in the mathematical formulations of stochastic optimization problems.
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Notes
- 1.
Notice that \(\mathfrak {R}^\infty \) is not the “limit” of \(\mathfrak {R}^n\) when \(n\) goes to infinity.
- 2.
The symbol \(\lnot \) denotes the negation operator .
- 3.
When \(\mathbb {Y}\) is a Borel space (see Sect. B.6), it is implicitely assumed that \(\mathcal {Y}\) is the \(\sigma \)-field \(\mathcal {B}_{\mathbb {Y}}^{\mathrm {o}}\) of Borel subsets.
- 4.
Indeed, if \(\mathbb {P}(\varOmega _j) = 0\), then the constant value \(u_j\) taken by the random variable
on \(\mathbb {P}(\varOmega _j)\) has no effect on the cost of the optimization problem (3.54).
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Carpentier, P., Chancelier, JP., Cohen, G., De Lara, M. (2015). Tools for Information Handling. In: Stochastic Multi-Stage Optimization. Probability Theory and Stochastic Modelling, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-319-18138-7_3
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DOI: https://doi.org/10.1007/978-3-319-18138-7_3
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