Constants in the asymptotics of small deviation probabilities for Gaussian processes and fields

This paper presents a survey of results on computing the small deviation asymptotics for Gaussian measures, that is, the asymptotics of the probabilities
$$ \mu(\varepsilon D), \qquad \varepsilon\to0, $$
where $D$ is a bounded domain in a Banach space $(B,{\|\cdot\|})$ (for example, $D=\{x\in B:\|x\|\leqslant 1\}$) and $\mu$ a Gaussian measure on $B$.
The main attention is focused on calculating the values of constants in the exact or logarithmic asymptotics. The survey contains new numerical results; some erroneous assertions in previous papers on this topic are also noted.
The following classes of Gaussian processes and fields are studied in detail: Wiener processes and related processes, Brownian bridges, Bessel processes, vector Wiener processes, Gaussian Markov processes, Gaussian processes with stationary increments, fractional Ornstein–Uhlenbeck processes, $n$-parameter fractional Brownian motion, $n$-parameter Wiener–Chentsov fields, and the Wiener pillow. Results on small deviations are presented in diverse norms, namely, the sup-norm, Hilbert norms, $L^p$-norms, Hölder norms, Orlicz norms, and weighted sup-norms.
About 30 problems concerned with finding exact constants in asymptotic expressions for small deviations are posed.
The relation to Chung's law of the iterated logarithm is also considered, and a number of other results are presented.