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.
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References
N. Bouleau, Autour de la variance comme forme de Dirichlet. Séminaire de Théorie du Potentiel 8 (Lect. Notes Math.) 1235, 39–53 (1989)
C. Dellacherie, S. MartÃnez, J. San MartÃn, D. Taïbi, Noyaux potentiels associés à une filtration. Ann. Inst. Henri Poincaré Prob. et Stat. 34, 707–725 (1998)
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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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DOI: https://doi.org/10.1007/978-3-319-10298-6_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10297-9
Online ISBN: 978-3-319-10298-6
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