List questions from filtrations

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Why is the following sigma algebra $\mathcal{F}_n=\pi_n^{-1}(\mathcal{B}(\{0,1\}^n))$ finite?

Published on 10 May 2026 - 13:08

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How can I show that $\mathcal{F}_t^X$ is generated by sets of the form $F=\{(X_{t_1},\dots, X_{t_n}) \in \Gamma\}$

Published on 29 Apr 2026 - 12:42

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Underlying Random Variable of Conditional Expectation

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What are the generating sets of $\mathcal{F}_t^X=\sigma(X_s , 0 \leq s \leq t) $?

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Where is the Strong Markov property(SM) being used in the proof that augmented filtration of a Strong Markov process is right continuous?

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Characterization of a set in the augmented filtration $\mathcal{F}_t^{\mu}=\sigma(\mathcal{F}_t^X, \mathcal{N}^{\mu})$

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Law of a Markov process uniquely determined by its 2-dimensional distributions

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Sub-sigma-algebras: infinite coin flips example on wikipedia

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Prove $(X_n, F_n) $ Martingale $\iff \int_{F} X_{n+1} = \int_{F} X_{n} \forall F \in F_n$

Published on 10 May 2026 - 13:16

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Are local martingales semimartingales in an enlarged filtration (under particular assumption)?

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Methods for filtering position signal

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Convergence in probability of conditional expectation

Published on 29 Apr 2026 - 12:42

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Largest filtration for a martingale

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Stopping time clarification

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List Question

$\sigma$-algebra generated by a subset of a set

Why is the following sigma algebra $\mathcal{F}_n=\pi_n^{-1}(\mathcal{B}(\{0,1\}^n))$ finite?

How can I show that $\mathcal{F}_t^X$ is generated by sets of the form $F=\{(X_{t_1},\dots, X_{t_n}) \in \Gamma\}$

Underlying Random Variable of Conditional Expectation

What are the generating sets of $\mathcal{F}_t^X=\sigma(X_s , 0 \leq s \leq t) $?

Where is the Strong Markov property(SM) being used in the proof that augmented filtration of a Strong Markov process is right continuous?

Characterization of a set in the augmented filtration $\mathcal{F}_t^{\mu}=\sigma(\mathcal{F}_t^X, \mathcal{N}^{\mu})$

Law of a Markov process uniquely determined by its 2-dimensional distributions

Sub-sigma-algebras: infinite coin flips example on wikipedia

Prove $(X_n, F_n) $ Martingale $\iff \int_{F} X_{n+1} = \int_{F} X_{n} \forall F \in F_n$

Are local martingales semimartingales in an enlarged filtration (under particular assumption)?

Methods for filtering position signal

Convergence in probability of conditional expectation

Largest filtration for a martingale

Stopping time clarification

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