L$_{p}$. Thus for pursuing a similar approach in spaces of generalized functions the following questions are addressed here: 1. Under what assumptions do the convolution equations hold? 2. When is Fourier transform and its inverse defined? 3. When does the exchange formula hold (and when is a multiplicative product defined)? 4. When do transformed equations have a unique solution? 5. When is the problem well-posed, that is the solution continuously depends on the known generalized functions in the equation? Once the conditions for identification and well-posedness are established in the generalized functions space, the question of consistent plug-in estima- tion can be examined. Suppose that the known functions, such as the den- sities (characteristic functions) of the observables, conditional expectations of the observables (and their Fourier transforms) in the models considered are consistently estimated; the solutions to the convolution equations based on these estimated functions are now random generalized functions; do they converge in some stochastic sense to the true function in the topology of generalized functions? In order to answer this one needs to consider stochastic generalized func- tions which represent stochastic functionals on the spaces of well behaved (differentiable, etc.) functions. These are described in Gel’fand and Vilenkin (1964) and Koralov and Sinai (2007). The question of consistency requires providing conditions for stochastic convergence of Fourier transforms and inverse Fourier transforms, of derivatives and of products for random gen- 11