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The effect on parametric instability growth of pump wave incoherence istreated by deriving a set of equations governing the space-time evolution ofthe ensemble-average coupled-mode amplitudes and intensities. Particularattention is paid to establishing the regions of validity of the statisticaldescription. Thresholds, growth rates, and amplification rates are given forboth spatially and temporally incoherent pump waves. Both absolutely andconvectively unstable modes are considered. The statistical results areverified where appropriate by numerical integration of the coupled-modeequations with different models of pump incoherence.

A Statistical Description of Parametric Instabilities with an Incoherent Pump