Importance of filtrations that are NOT natural filtrations. The Next CEO of Stack...
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Importance of filtrations that are NOT natural filtrations.
The Next CEO of Stack OverflowGenerated sigma algebra from Brownian MotionConditional events that are not in the event algebra?Examples for Conditional Expectation (modern probability theory)How does the natural filtration of a Brownian motion look like?Filtrations and Sigma-Algebras and Stopping TimesIntuition behind measurable random variables and $sigma$-algebraBayes Theorem: what is wrong in using counts instead, intuitively.Mapping from natural filtration to sequence of events $X(t)$adapted process, translation between measurable and information?Is every filtration the natural filtration of some stochastic process?
$begingroup$
I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional expectations (say).
But what's the motivation/significance of the concept of a filtration (i.e. an increasingly sequence of sub-sigma algebras) in general?
Put differently, why would one be interested in filtrations that are not natural filtrations?
probability measure-theory filtrations
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
$endgroup$
add a comment |
$begingroup$
I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional expectations (say).
But what's the motivation/significance of the concept of a filtration (i.e. an increasingly sequence of sub-sigma algebras) in general?
Put differently, why would one be interested in filtrations that are not natural filtrations?
probability measure-theory filtrations
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
$endgroup$
add a comment |
$begingroup$
I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional expectations (say).
But what's the motivation/significance of the concept of a filtration (i.e. an increasingly sequence of sub-sigma algebras) in general?
Put differently, why would one be interested in filtrations that are not natural filtrations?
probability measure-theory filtrations
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
$endgroup$
I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional expectations (say).
But what's the motivation/significance of the concept of a filtration (i.e. an increasingly sequence of sub-sigma algebras) in general?
Put differently, why would one be interested in filtrations that are not natural filtrations?
probability measure-theory filtrations
probability measure-theory filtrations
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
edited Mar 17 at 18:02
Dhruv Gupta
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
asked Mar 17 at 17:48
Dhruv GuptaDhruv Gupta
818
818
add a comment |
add a comment |
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