  A result of Arcones implies that if a measure-preserving linear operator $S$
on an abstract Wiener space $(X,H,\mu)$ is strongly mixing, then the set of
limit points of the random sequence $((2\log n)^{-1/2}S^n(x))_{n\in\mathbb N}$
equals the unit ball of $H$ for a.e. $x \in X$, which may be seen as a
generalization of the classical Strassen's law of the iterated logarithm. We
extend this result to the case of a continuous parameter $n$ and higher
Gaussian chaoses, and we also prove a contraction-type principle for Strassen
laws of such chaoses. We then use these extensions to recover or prove
Strassen-type laws for a broad collection of processes derived from a Gaussian
measure, including "nonlinear" Strassen laws for singular SPDEs such as the KPZ
equation.
