Abstract
For an arbitrary poset H and measure ρ on H × R (where R is the real axis), we construct a monotone decreasing stochastic field ηρ and compute its finite-dimensional distributions. In the case where H is a Λ-semilattice and the measure ρ satisfies additional conditions, we compute various characteristics of the field ηρ such as the expectation of the field value at a point, variance of the field value at a point, and correlation function of the field. The described construction of random fields gives a new method for constructing positive definite functions on posets. Bibliography: 6 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 301, 2003, pp. 92–143.
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Beinenson, L.B. Monotone Nonincreasing Random Fields on Partially Ordered Sets. I. J Math Sci 129, 3730–3756 (2005). https://doi.org/10.1007/s10958-005-0310-0
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DOI: https://doi.org/10.1007/s10958-005-0310-0