List questions from filtrations

Published on 20 Oct 2022 - 15:26

357

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Is $Z_n = X_n Y_n$ a martingale?

Published on 03 Nov 2022 - 15:56

49

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Is $E[X_sX_t^2]=0 \,\,s<t$ for a MDS?

Published on 10 Nov 2022 - 22:15

150

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Algebra is noetherian if associated graded algebra is noetherian

Published on 25 Mar 2026 - 16:01

114

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Rees algebra is finitely generated if associated graded algebra is

Published on 25 Mar 2026 - 17:45

33

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Calculate $E[X_t|\mathcal{F}_s^X]$ for each $s < t$

Published on 22 Nov 2022 - 19:10

64

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Equivalent Definitions of Hodge Structure

Published on 23 Nov 2022 - 8:52

168

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Prove that $T$ is a stopping time

Published on 24 Nov 2022 - 13:56

496

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Stochastic processes: understanding a complete filtration

Published on 10 Dec 2022 - 14:04

62

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Definition of $\mathcal{F}_{t-}$

Published on 10 Dec 2022 - 21:51

261

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A stochastic process with right continuous paths and usual conditions to the adapted filtration is progressively measurable

Published on 19 Dec 2022 - 14:06

120

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Example of a progressively measurable process not optional

Published on 21 Dec 2022 - 17:14

104

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Harder-Narasimhan filtration of tensor product of coherent sheaves

Published on 02 Jan 2023 - 15:01

186

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$\sigma$-algebra of $\tau$-past: Definition vs interpretation

Published on 06 Jan 2023 - 14:58

79

Views

Showing that the stopped filtration $\mathcal{F}_{s \wedge t} = \mathcal{F}_s \cap \mathcal{F}_t$

Published on 08 Jan 2023 - 9:38

List Question

Expectation of Brownian Motion adapted for Filtration

Is $Z_n = X_n Y_n$ a martingale?

Is $E[X_sX_t^2]=0 \,\,s<t$ for a MDS?

Algebra is noetherian if associated graded algebra is noetherian

Rees algebra is finitely generated if associated graded algebra is

Calculate $E[X_t|\mathcal{F}_s^X]$ for each $s < t$

Equivalent Definitions of Hodge Structure

Prove that $T$ is a stopping time

Stochastic processes: understanding a complete filtration

Definition of $\mathcal{F}_{t-}$

A stochastic process with right continuous paths and usual conditions to the adapted filtration is progressively measurable

Example of a progressively measurable process not optional

Harder-Narasimhan filtration of tensor product of coherent sheaves

$\sigma$-algebra of $\tau$-past: Definition vs interpretation

Showing that the stopped filtration $\mathcal{F}_{s \wedge t} = \mathcal{F}_s \cap \mathcal{F}_t$

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