Colored noise: A case study of the cumulant method

The time ordered operator cumulant expansion (R. Kubo, R.F. Fox) is one of the standard tools for treating classical or quantum systems influenced by colored noise. Because of its poor convergency properties, partial summations become imperative if the noise is not weak. A recently developed resummed version of the cumulant expansion is shown in the present paper to yield in a conventional way correct physical results in situations where the cumulant expansion extended to the fourth cumulant drastically fails. The theory amounts to a renormalization procedure of the bare physical parameters occurring in the second cumulant expression.