Asymptotical power of convolutional tests of symmetry and homogeneity. Financial applications in “disorder” detection

Two new tests of symmetry and three new tests of homogeneity based on convolutional statistics distributions have been constructed. Their properties have been comparatively described. Stochastic integral of anticipatory function has been defined. Characteristic functions of power of convolutional symmetry test based on the integral of anticipatory function (second type convolution) and on the first type convolution have been calculated for any continuous alternative. Applications in financial mathematics have been given (financial control charts and “disorder” quickest detection problem). All results are new.