Abstract
The purpose of this chapter is to provide a brief overview of the key mathematical ways of thinking that underpin our presentation of the subject of data assimilation . In particular, we touch on the subjects of probability, dynamical systems, probability metrics, and dynamical systems for probability measures, in Sections 1.1, 1.2, 1.3, and 1.4 respectively. Our treatment is necessarily terse and very selective, and the bibliography section 1.5 provides references to the literature.
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Notes
- 1.
Of course, μ and ρ depend on the particular random variable z, but we suppress this dependence in the notation.
- 2.
Sometimes also called a normal random variable .
- 3.
This discussion is easily generalized to \(j \in \mathbb{Z}^{+}\).
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Law, K., Stuart, A., Zygalakis, K. (2015). Mathematical Background. In: Data Assimilation. Texts in Applied Mathematics, vol 62. Springer, Cham. https://doi.org/10.1007/978-3-319-20325-6_1
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DOI: https://doi.org/10.1007/978-3-319-20325-6_1
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