Quasiasymptotics in exponential distributions by wavelet analysis (Q1944661)

The author considers a standard MRA within the space of square-integrable functions on the real line. The MRA expansion is then applied to exponential distributions. The aim is to analyze the properties at a point (i.e. quasiasymptotics) of such distributions with the help of the MRA expansion. The main result is that under some regularity properties one can achieve quasiasymptotics at a point (a similar result is also proved at infinity) of the continuous type if and only if the same property holds for every projection of the distribution on the elements of the MRA. It is known that the corresponding comparison function (which is continuous in this case) has also to be a regularly varying function. In the case that the distribution is quasiasymptotically bounded at zero, the results are applied to orthonormal wavelets, and some specific upper bounds for the corresponding wavelet coefficients are derived.