a stochastic process $$\begin{aligned}
X_{t} = \left( X_{t}^{(1)},\ldots, X_{t}^{(d)}\right) , \quad t \in[0, T],\end{aligned}$$ which denotes a centered (i.e. zero-mean), continuous Gaussian process in $\mathbb{R}^{d}$ with i.i.d. components.

This process is defined on the canonical probability space $\left(\Omega,\mathcal{F},\mathbb{P}\right)  $, where $\Omega=\mathcal{C}\left(
[0,T];\mathbb{R}^{d}\right) $, the space of continuous $\mathbb{R}^d$-valued paths equipped with the supremum topology, $\mathcal{F}$ is the completion of the Borel $\sigma$-algebra generated by $X$, and $\mathbb{P}$ is the unique Borel measure under which $X \left( \omega\right) = \left( \omega_{t}\right)_t \in \left[ 0, T\right] $ has the specified Gaussian distribution. We will use $$\begin{aligned}
R(s,t):=\mathbb{E}\left[ X_{s}^{(1)}X_{t}^{(1)}\right]\end{aligned}$$ to denote the covariance function common to the components. The variance $R\left( t, t\right) $ will be denoted simply by $R(t)$, and we will also use the notation $$\begin{aligned}
\sigma^{2}(s,t):=R
\begin{pmatrix}
s & t\\
s & t
\end{pmatrix}
=\mathbb{E}\left[ \left(  X_{s,t}^{(1)}\right)^{2}\right];\end{aligned}$$ recall the definition of the rectangular increment in .

The triple $\left(  \Omega,\mathcal{H}^{d},\mathbb{P} \right)  $ denotes the abstract Wiener space associated to $X$, where $\mathcal{H}^{d}=\bigoplus_{i=1}^{d}\mathcal{H}$ is the Cameron-Martin space (or reproducing kernel Hilbert space). The Cameron-Martin space, which is densely and continuously embedded in $\Omega\text{,}$ is the completion of the linear span of the functions $$\begin{aligned}
\left\{  R(t, \cdot)^{(u)} := R(t,\cdot) \, e_{u} 