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Filtered Matrices

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Part of the Lecture Notes in Mathematics book series (LNM,volume 2118)

Abstract

In this chapter we introduce certain notions that are frequent in probability theory and stochastic analysis, which prove fruitful in describing inverse M-matrices. A main concept is mean conditional expectation matrix. This type matrices is the linear version of partitions and they satisfy the complete maximum principle, so they are natural objects in theory of inverse M-matrices. Additionally, they are also projections that preserve positivity and the constant vectors.

Keywords

  • Conditional Expectation
  • Spectral Decomposition
  • Nonnegative Matrix
  • Block Form
  • Hadamard Product

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. N. Bouleau, Autour de la variance comme forme de Dirichlet. Séminaire de Théorie du Potentiel 8 (Lect. Notes Math.) 1235, 39–53 (1989)

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  2. C. Dellacherie, S. Martínez, J. San Martín, D. Taïbi, Noyaux potentiels associés à une filtration. Ann. Inst. Henri Poincaré Prob. et Stat. 34, 707–725 (1998)

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© 2014 Springer International Publishing Switzerland

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Dellacherie, C., Martinez, S., San Martin, J. (2014). Filtered Matrices. In: Inverse M-Matrices and Ultrametric Matrices. Lecture Notes in Mathematics, vol 2118. Springer, Cham. https://doi.org/10.1007/978-3-319-10298-6_5

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