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Recovering a Family of Two-Dimensional Gaussian Variables from the Minimum Process

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  • Irene Hueter

    (University of Florida)

Abstract

Suppose that {(X t, Y t): t>}0 is a family of two independent Gaussian random variables with means m 1(t) and m 2(t) and variances σ 2 1(t) and σ 2 2(t). If at every time t>0 the first and second moment of the minimum process X t∧Y t are known, are the parameters governing these four moment functions uniquely determined ? We answer this question in the negative for a large class of Gaussian families including the “Brownian” case. Except for some degenerate situation where one variance function dominates the other, in which case the recovery of the parameters is fully successful, the second moment of the minimum process does not provide any additional clues on identifying the parameters.

Suggested Citation

  • Irene Hueter, 2000. "Recovering a Family of Two-Dimensional Gaussian Variables from the Minimum Process," Journal of Theoretical Probability, Springer, vol. 13(4), pages 939-950, October.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:4:d:10.1023_a:1007822806163
    DOI: 10.1023/A:1007822806163
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    References listed on IDEAS

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    1. Mukherjea, A. & Nakassis, A. & Miyashita, J., 1986. "The problem of identification of parameters by the distribution of the maximum random variable," Journal of Multivariate Analysis, Elsevier, vol. 18(2), pages 178-186, April.
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    3. Mukherjea, Arunava & Stephens, Richard, 1990. "The problem of identification of parameters by the distribution of the maximum random variable: Solution for the trivariate normal case," Journal of Multivariate Analysis, Elsevier, vol. 34(1), pages 95-115, July.
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