Filtration (mathematics)

In mathematics, a filtration is an indexed set S_i of subobjects of a given algebraic structure S, with the index i running over some index set I that is a totally ordered set, subject to the condition that

If the index i is the time parameter of some stochastic process, then the filtration can be interpreted as representing all historical but not future information available about the stochastic process, with the algebraic object S_i gaining in complexity with time. Hence, a process that is adapted to a filtration , is also called non-anticipating, i.e. one that cannot see into the future.