Bifurcation in a random environment

(Received 15 May 1992, accepted in final form 30 May 1992)

Abstract
I investigate various instances of bifurcation in a random stationary environment. This is done for a model equation, with a bifurcation parameter fluctuating in space. The noise is either Gaussian or two states Poisson. I estimate then the order parameter as a function of a bifurcation parameter. This is mostly done by Lifshitz-tail type estimates on the linear part of the equation. However, near the threshold of instability in the absence of noise, this one-whatever small it is-becomes important and there the nonlinearity becomes crucial too.