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This research aims to establish a Gnedenko-type limit theorem for the maximums of stationary Gaussian processes that include a linear trend.

April 3, 2026Mathematical Notes

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

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This research aims to establish a Gnedenko-type limit theorem for the maximums of stationary Gaussian processes that include a linear trend.
Derived a limit theorem for maximum values of the defined process.
Analyzed the behavior of the process $$X(t)=\xi(t)-ct^eta$$ under specific conditions.
Considered stationary Gaussian processes with defined constants c and beta.
The theorem characterizes the distribution of the maximum values of the process.
Shows convergence towards a specific limiting behavior for large time scales.

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Implication

A theorem demonstrates the behavior of maximum values in stationary Gaussian processes with a trend, suggesting clear implications for statistical modeling.

Cite This Study

Goran Popivoda (2025) studied this question.

synapsesocial.com/papers/69cf5e015a333a821460c093 https://doi.org/10.1134/s0001434624605938

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Implication

A theorem demonstrates the behavior of maximum values in stationary Gaussian processes with a trend, suggesting clear implications for statistical modeling.

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

Key Points

Discussion

Implication

Cite This Study

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

Key Points

Discussion

Implication

Cite This Study

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