Summary
LetX(t), 0≦t≦1, be a Gaussian process with mean 0 and continuous covariance function. Put σ2(t)=EX 2(t), and suppose that there is a point τ in [0, 1] such that σ2(t) has unique maximum att=τ. PutL u =mes(s: 0≦s≦1,X(s)>u). Under suitable conditions there exists a functionv=v(u) and a distribution functionG(x), x>0, such thatv(u)→∞ foru→∞, and
References
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This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship of the National Science Foundation, Grants MCS 82. 01119 and DMS 85 01512
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Berman, S.M. Extreme sojourns of a Gaussian process with a point of maximum variance. Probab. Th. Rel. Fields 74, 113–124 (1987). https://doi.org/10.1007/BF01845642
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DOI: https://doi.org/10.1007/BF01845642
Keywords
- Covariance
- Stochastic Process
- Probability Theory
- Mathematical Biology
- Covariance Function