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Gaussian functions / distributions / processes...

3 votes
0 answers
318 views

Equivalence of Gaussian measures on Hilbert space

Suppose we have 2 nondegenerate Gaussian measures given by N(0,T) and N(0,S) supported on a separable Hilbert space H. … Does there exist a permutation of set of eigenpairs of S such that the resulting Gaussian measure(after the permutation) is absolutely continuous wrt N(0,T)? …
6 votes
2 answers
611 views

If Gaussian measures on a Hilbert space converge weakly to 0, how do their covariance operat...

Suppose we have a sequence of Gaussian measures $N(0, S(n))$ supported on a Hilbert space $H$ and we know that the sequence converges weakly to the delta measure at $0$, what are the necessary and sufficient …