NEW APPROACH TO MULTIPLICATIVE STOCHASTIC-PROCESSES .2. INFINITE NUMBER OF TIME CORRELATIONS

Time correlation of fluctuations generated by a multiplicative stochastic dynamics is investigated from a new statistical-mechanical viewpoint. The overall characteristics of temporal correlations are shown to be singled out with the order-q power spectrum I(q)(omega) and the order-q time correlation function C(q)(t) with a parameter q, the degree of ensemble processing, by solving the eigenvalue problem of the generalized Fokker-Planck operator H(q). Their asymptotic forms in different q-regions are obtained. We find that as the value of q is decreased the time correlation function changes from the exponential decay to a power law form at a certain critical point of q. This transition is discussed in connection with the development of intermittency, observed in a coupled, chaotic electronic circuit, and in chaotic systems.