Final Report Summary - SCHREC (Stochastic recursions and limit theorems)
We considered a d-dimensional non-linear stochastic recursion which generalises a 1-dimensional (1D) one already considered by Durrett-Liggett, Kahane-Peyrière and Mandelbrot. The aim was to obtain the conditions for existence of a solution and to study its tail properties. We were able to obtain the necessary and sufficient condition of existence and to show its homogeneity at infinity, using the properties of products of random matrices. Analogous problems appear in various domains, including mathematical statistics, fractal analysis, statistical mechanics and closely related methods could be used. Also, the results could be useful in computer science.
