An overdamped system with a linear restoring force and two multiplicative
colored noises is considered. Noise amplitudes depend on the system state x
as x and ∣x∣α. An exactly soluble model of a system is constructed
due to consideration of a specific relation between noises. Exact expressions
for the time-dependent univariate probability distribution function and the
fractional moments are derived. Their long-time asymptotic behavior is
investigated analytically. It is shown that anomalous diffusion and stochastic
localization of particles, not subjected to a restoring force, can occur.Comment: 15 page