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I do encounter the following terms in a number of academic journal papers:

"For a softening process, the third order Hermite functional transformation is ..."

Efficient stationary multivariate non-Gaussian simulation based on a Hermite PDF model

Similarly, for instance, the following:

"This study presents a moment-based translation model for hardening non-Gaussian processes with kurtosis less than three."

Moment-Based Translation Model for Hardening Non-Gaussian Response Processes

What do softening/hardening a process mean?

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Another journal paper seems to explain the terms:

"Based on whether kurtosis is larger than 3, the non-Gaussian process is classified as “hardening” (kurtosis<3) and “softening” (kurtosis>3) cases"

Revisiting moment-based characterization for wind pressures

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