Adapted Process

A Adapted Process is a stochastic process that is adapted to some filtration.

• AKA: Non-anticipating Process , Non-anticipative Process.
• Context:
  • It can be defined as: "A stochastic process [math]\displaystyle{ X = (X_t, t \geq 0) }[/math] is said to be an adapted process to the filtration of sigma algebra ([math]\displaystyle{ F }[/math]), i.e. [math]\displaystyle{ (F_t, t \geq 0) }[/math] if [math]\displaystyle{ \sigma (X_t) \subseteq F_t ,\; \forall t \geq 0" }[/math],
• Counter-Example(s):
  • Progressive Process.
• See: Stochastic process, Progressively Measurable Process, Filtration, Open Sets, Sigma Algebra.

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References

2016

• (Wikipedia, 2016) ⇒ https://www.wikiwand.com/en/Adapted_process Retrieved 2016-07-24
  • In the study of stochastic processes, an adapted process (also referred to as a non-anticipating or non-anticipative process) is one that cannot "see into the future". An informal interpretation of an adapted process is essential, for instance, in the definition of the Itō integral, which only makes sense if the integrand is an adapted process.

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