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user47295
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Equivalence of Gaussian measures on Hilbert space
I meant N(0,R'SR).
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Equivalence of Gaussian measures on Hilbert space
Both Gaussians are non degenerate(just made the edit). @nate yes, I mean an operator R which permutes eigenvectors of S and the resulting Gaussian is N(0,SR).
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Equivalence of Gaussian measures on Hilbert space
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Equivalence of Gaussian measures on Hilbert space
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If Gaussian measures on a Hilbert space converge weakly to 0, how do their covariance operators converge?
Thankyou Nate. The edit and the example both were most helpful.
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If Gaussian measures on a Hilbert space converge weakly to 0, how do their covariance operators converge?
Thank you for the answer. So, the necesssary and sufficient condition would be convergence in trace class norm and even the operator norm is not sufficient.
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If Gaussian measures on a Hilbert space converge weakly to 0, how do their covariance operators converge?
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If Gaussian measures on a Hilbert space converge weakly to 0, how do their covariance operators converge?