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Abstract <p> A Gnedenko-type limit theorem is derived for the maximum of the process <Equation ID="Equi"> <EquationSource Format="TEX">\(X(t)=\xi(t)-ct^\beta,\)</EquationSource> </Equation> where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\xi(t)\)</EquationSource> </InlineEquation> is a stationary Gaussian process and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(c\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\beta\)</EquationSource> </InlineEquation> are positive constants. </p>

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Gnedenko-Type Limit Theorem for the Maximum of Stationary Gaussian Processes with a Trend

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • G. Popivoda

摘要

Abstract

A Gnedenko-type limit theorem is derived for the maximum of the process \(X(t)=\xi(t)-ct^\beta,\) where \(\xi(t)\) is a stationary Gaussian process and \(c\) and \(\beta\) are positive constants.