= Solution
The assertion is true. The <Dambis-Dubins-Schwarz theorem>, with an independent continuation of the Brownian motion if $f$ is bounded, represents
$$
M_t=W_{[M]_t}=W_{f(t)}.
$$
Because $f$ is deterministic, every finite vector $(M_{t_1},\ldots,M_{t_n})$ is a finite vector of a <Brownian motion> at deterministic times and therefore has a <multivariate normal distribution>. Hence $M$ is a <Gaussian process>. This is the <deterministic quadratic variation characterizes a Gaussian continuous local martingale> result.
Back to article page
