Filtration (probability theory)

In the theory of stochastic processes, a subdiscipline of probability theory, filtrations are totally ordered collections of subsets that are used to model the information that is available at a given point and therefore play an important role in the formalization of random (stochastic) processes. == Definition == Let ( Ω , A , P ) {\displaystyle (\Omega ,{\mathcal {A}},P)} be a probability space and let I {\displaystyle I} be an index set with a total order ≤ {\displaystyle \leq } (often N {\displaystyle \mathbb {N} } , R + {\displaystyle \mathbb {R} ^{+}} , or a subset of R + {\displaystyle \mathbb {R} ^{+}} ).

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