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Henry.L
Henry.L
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square Square integrable conditional expectationexpectations as projectionprojections

I see this page Ordinary least square and random projection, and I am thinking that how L^2$L^2$ integrable random variables be regarded as projections over a defined filtration \mathcal{F_n}sequence $\mathcal{F_n}$ ? 

It seems that a vector space of square integrable random variables defined on the same probability space is not enough? Is Is there existing literature addressing a formalism of this projection view? Thank you!

square integrable conditional expectation as projection

I see this page Ordinary least square and random projection, and I am thinking that how L^2 integrable random variables be regarded as projections over a defined filtration \mathcal{F_n} ? It seems that a vector space of square integrable random variables defined on the same probability space is not enough? Is there existing literature addressing a formalism of this projection view? Thank you!

Square integrable conditional expectations as projections

I see this page Ordinary least square and random projection, and I am thinking that how $L^2$ integrable random variables be regarded as projections over a defined filtration sequence $\mathcal{F_n}$ ? 

It seems that a vector space of square integrable random variables defined on the same probability space is not enough? Is there existing literature addressing a formalism of this projection view? Thank you!

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lsn
lsn
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square integrable conditional expectation as projection

I see this page Ordinary least square and random projection, and I am thinking that how L^2 integrable random variables be regarded as projections over a defined filtration \mathcal{F_n} ? It seems that a vector space of square integrable random variables defined on the same probability space is not enough? Is there existing literature addressing a formalism of this projection view? Thank you!