NON-LINEAR TRANSFORMATIONS OF MEASURES IN PROBLEMS OF STICHASTIC ANALYSIS

The work is to devoted to studying non-linear transformations of the measures in the infinite-dimensional spaces and also to the problem about smoothness of the measures connected with diffusions. It has been proven that the distribution of the smooth diffusion in C[0,1] cannot be exclusive according to Aronshine; if it is not equivalent to the Wiener measure is is mutual-singular with any measure having only one non-zero direction of the continuity. It has been shown also that in the Hilbert space the smooth diffusion can possesses the invariant measures and transfer probabilities without directions of the continuity. The example of the continuous polynomial transformation in the Hilbert ball without unmovable points, which in this case has the invariant measures has been constructed. The results can find application in the different problems of the infinite-dimensional analysis and stochastics and their applications. The methods for analytical theory of measure, non-linear functional analysis and stochastic analysis have been used. A number of the special developed structures has been applied.Available from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio