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The response of a building structure to gusty wind is formulated as a nonlinear problem in which random inputs occur both as parametric and nonparametric excitations. The stationary probability density is obtained for the structural motion parallel to the direction of the average wind velocity, from which the criteria for in-probability stability and various moment stabilities can be determined. The transient (nonstationary) second moment of the response in this direction is also obtained. For the structural motion perpendicular to the average wind velocity only the first moment stability boundary can be computed, and this boundary reduces to one corresponding to the known deterministic theory when the turbulence terms are dropped.
Ye et al. (1978) studied this question.