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This is clearly a question involving 2 Gaussian measures(Also, I asked this question)
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edit approved Jun 24, 2014 at 9:00
user53215
edit approved Jun 24, 2014 at 9:00
user53215
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user47295
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Suppose we have 2 nondegenerate Gaussian measures given by N(0,T) and N(0,S) supported on a separable Hilbert space H. T and S are such that eigenbasis of S lies in the cameron martin space of N(0,T). Furthermore, let S and T have the same eigenvalues. 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)?

Suppose we have 2 Gaussian measures given by N(0,T) and N(0,S) supported on a separable Hilbert space H. T and S are such that eigenbasis of S lies in the cameron martin space of N(0,T). Furthermore, let S and T have the same eigenvalues. 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)?

Suppose we have 2 nondegenerate Gaussian measures given by N(0,T) and N(0,S) supported on a separable Hilbert space H. T and S are such that eigenbasis of S lies in the cameron martin space of N(0,T). Furthermore, let S and T have the same eigenvalues. 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)?

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user47295
user47295
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Equivalence of Gaussian measures on Hilbert space

Suppose we have 2 Gaussian measures given by N(0,T) and N(0,S) supported on a separable Hilbert space H. T and S are such that eigenbasis of S lies in the cameron martin space of N(0,T). Furthermore, let S and T have the same eigenvalues. 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)?