Filtration (mathematics)

（重定向自Filtered group）

In mathematics, a filtration $\mathcal{F}$ 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 $\mathcal{F}$ , is also called non-anticipating, i.e. one that cannot see into the future.

单词	Filtered group
释义	Filtered group 英语百科 Filtration (mathematics) （重定向自Filtered group） In mathematics, a filtration $\mathcal{F}$ 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 $\mathcal{F}$ , is also called non-anticipating, i.e. one that cannot see into the future.
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