Every linear combination of $X_{t_1},\ldots,X_{t_n}$ is a deterministic constant plus one stochastic integral of a deterministic $L^2$ function against $B$. Part a makes every such combination Gaussian. By the linear-combination characterization of a <multivariate normal distribution>, $(X_{t_1},\ldots,X_{t_n})$ is jointly Gaussian, so $X$ is a <Gaussian process>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 202 / 6 / d / Solution

 Solution (source code)