List questions from filtrations

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How to calculate sigma algebra generated by random variables in stochastic process?

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Stopping-time sigma-algebra and the case at infinity, definition question.

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Filtered objects and associated graded objects

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Exhaustive filtration of a torsion abelian group

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Is $\mathcal{F}_\infty$ a $\sigma$-algebra? (Chung Theorem 9.4.8.)

Published on 28 Apr 2017 - 17:18

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Show that for complete and right-continuous filtration, and $\sigma = \tau$ a.s. with $\tau$ stopping time, then $\sigma$ stopping time

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Example of filtration in probability theory

Published on 13 May 2017 - 12:35

784

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For a discrete stopping time $\tau$, $\mathcal{F}_\tau^X = \sigma(X(t\wedge\tau):t\ge 0).$

Published on 12 Jun 2017 - 15:56

584

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How can we show that $\mathcal F_\tau\cap\left\{\tau=t\right\}=\mathcal F_t$? for any $\mathcal F$-stopping time $\tau$?

Published on 13 Jun 2017 - 19:51

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Conditional expectation on a filtration defined by a stopping time

Published on 20 Jun 2017 - 20:15

105

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Commutation between σ-algebra and intersection

Published on 21 Jul 2017 - 3:41

121

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Mapping from natural filtration to sequence of events $X(t)$

Published on 03 Aug 2017 - 23:12

106

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The associated graded of a filtered coalgebra

Published on 25 Mar 2026 - 12:43

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A philosophical question about filtrations and information sets

Published on 17 Aug 2017 - 23:38

List Question

Isomorphism of Filtered Objects?

How to calculate sigma algebra generated by random variables in stochastic process?

Stopping-time sigma-algebra and the case at infinity, definition question.

Filtered objects and associated graded objects

Exhaustive filtration of a torsion abelian group

Is $\mathcal{F}_\infty$ a $\sigma$-algebra? (Chung Theorem 9.4.8.)

Show that for complete and right-continuous filtration, and $\sigma = \tau$ a.s. with $\tau$ stopping time, then $\sigma$ stopping time

Example of filtration in probability theory

For a discrete stopping time $\tau$, $\mathcal{F}_\tau^X = \sigma(X(t\wedge\tau):t\ge 0).$

How can we show that $\mathcal F_\tau\cap\left\{\tau=t\right\}=\mathcal F_t$? for any $\mathcal F$-stopping time $\tau$?

Conditional expectation on a filtration defined by a stopping time

Commutation between σ-algebra and intersection

Mapping from natural filtration to sequence of events $X(t)$

The associated graded of a filtered coalgebra

A philosophical question about filtrations and information sets

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