= Exponential tilting of an isonormal Gaussian process
{title2=$d\mathbb Q/d\mathbb P=e^{X(k)-\|k\|^2/2}$}
= Gaussian exponential tilt
{c}
{synonym}
For an <isonormal Gaussian process> $X$ on a real <Hilbert space> $H$ and $k\in H$, the positive density $\exp(X(k)-\|k\|^2/2)$ has expectation one and defines an <equivalent probability measure>. Under this measure, $X(h)$ has mean $\langle h,k\rangle$ and the same <covariance> as before. The shifted family $X(h)-\langle h,k\rangle$ is again an <isonormal Gaussian process>. This follows by evaluating the joint Gaussian exponential formula for any finite collection of arguments. It is the Hilbert-space version of <exponential tilting>.
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