Boris Tsirelson,
"Moderate deviations for log-like functions of stationary Gaussian processes."
arXiv:math.PR/0703289.
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/math.PR/0703289/
or its Israeli mirror:
il.arXiv.org/abs/math.PR/0703289/

A research eprint, 25 pages, bibl. 5 refs.

A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.) Both discrete and continuous time is treated. An integrable power-like decay of the correlation function is assumed.

1. Introduction.
1. Assumptions on the (nonlinear) function.
2. Assumptions on the Gaussian process.
3. The result.
4. Splitting the process.
5. A small deviation argument.
6. Surgery.
7. Asymptotic variance.
8. Asymptotic exponential moments.