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Filtration

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Summary

An increasing indexed family of σ\sigma-algebras representing information over time.

Record metadata

Carrier(s)

Data

Axioms / constraints

Notes

A filtration is a monotone family of sub-σ\sigma-algebras of one ambient measurable space, indexed by an ordered set.

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

ordered family + ambient measurable space(construction junction)Filtration

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Require monotonicity FsFt\mathcal F_s\subseteq\mathcal F_t for sts\le t within one ambient σ\sigma-algebra.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Filtrationprobability + filtration(construction junction)

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Supply the Filtration structure as one jointly required input.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources