Timeline for coupling of projections and projection of the coupling
Current License: CC BY-SA 3.0
6 events
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| Nov 24, 2012 at 19:39 | comment | added | R W | What you call "coupling" is known in ergodic theory as "joining". As far as I understand, in probability coupling is defined for measures on product spaces and requires an additional property: when projected onto the coordinate spaces $X_n^\infty$ (only the coordinates with indices $\ge n$ are retained), the images of the measure $C$ converge to the diagonal measure in total variation. Could you please clarify your definition of coupling. | |
| Nov 24, 2012 at 16:36 | comment | added | QuantumLogarithm | I want to prove that the projection of a certain coupling between two measures on a certain coordinate of the product space is equal to the coupling between the projection of the two measures on the same coordinate. The coupling operator is the same in the two cases, but in the first case it acts on the two measures and later one considers the projection, while in the second case it acts directly on the projection of the two measures. | |
| Nov 24, 2012 at 16:35 | history | edited | QuantumLogarithm | CC BY-SA 3.0 |
I changed a sentence to make a bit more clear the statement, in case it was not completely clear before.
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| Nov 24, 2012 at 10:46 | history | edited | QuantumLogarithm | CC BY-SA 3.0 |
added 384 characters in body; edited body
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| Nov 23, 2012 at 20:10 | comment | added | Anthony Quas | Not sure what you mean by "the projection of the coupling is the coupling of the projections"? Do you mean is a coupling of the projections? | |
| Nov 23, 2012 at 17:41 | history | asked | QuantumLogarithm | CC BY-SA 3.0 |