ABSTRACT
The notion of filtration is used to represent, for example, the flow of possible observations of prices on a financial market which is available for traders and portfolio managers.
DEFINITION B.1 Suppose (Ω,F ,P) is a probability space. A filtration (Ft)t is an increasing family of sub-sigma-fields Ft ⊂ F . A
stochastic basis is a probability space equipped with a filtration. Increasing means that if s ≤ t, then Fs ⊂ Ft. Ft is usually interpreted as the set of events that occur before or at time t. Generally, Ft represents the history of some process observed up to time t, but other possible histories are allowed.
