# Concept derivation guides

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Concept guide



## [Finite filtration: checking information nesting by partition refinement, and separating it from adaptedness and independence](/en/derivations/derivation-mko-finite-filtration-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-finite-filtration)

On Ω={0,1,2,3} (two coin tosses: 0=HH, 1=HT, 2=TH, 3=TT), represent the σ-algebras at times 0, 1, 2 by partition rows P_0, P_1, P_2. Prove that 'the later partition refines the earlier one ⇔ the σ-algebras are nested', check every adjacent pair of times completely and conclude that (F_t) is a filtration; give a sequence of partitions that is not a filtration; and show that a filtration neither makes every process adapted nor implies independence.

Finite filtration

derivation-mko-finite-filtration-01





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