Critical Slowing Down in Stochastic Processes. I

Abstract

The present series of papers clarify the physical mechanism of a critical slowing down in stochastic processes. It is classified into three categories, namely (i) deterministic, (ii) marginal and (iii) noise-induced critical slowing downs. In this paper, some general aspects of critical slowing down are studied in multiplicative processes. The value of the long-time exponent is derived on the basis of the dynamical scaling theory for general nonlinear stochastic processes as well as conditions for the appearance of the noise-induced long-time tail. Some exactly soluble examples are discussed.