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The present paper establishes convolution theorems for regular estimatorswhen the limit experiment is non-Gaussian or of infnite dimension with sparseparameter space. Applications are given for Gaussian shift experiments ofinfnite dimension, the Brownian motion signal plus noise model, Levy processeswhich are observed at discrete times and estimators of the endpoints ofdensities with jumps. The method of proof is also of interest for the classicalconvolution theorem of Hajek and Le Cam. As technical tool we present anelementary approach for the comparison of limit experiments on standard Borelspaces.

The Convolution Theorem of Hajek and Le Cam - Revisited