adapted process

Let {XttT} be a stochastic processMathworldPlanetmath defined on a probability spaceMathworldPlanetmath (Ω,,P) and {ttT} a filtrationPlanetmathPlanetmath (an increasing sequence of sigma subalgebras of ), where T is a linearly ordered subset of with a minimum t0. Then the process {Xt} is said to be adapted to the filtration {t} if for each tt0, Xt is t-measurable (

Xt-1(B)t for each Borel set B.

A stochastic process is an adapted process if it is adapted to some filtration.

Title adapted process
Canonical name AdaptedProcess
Date of creation 2013-03-22 16:16:43
Last modified on 2013-03-22 16:16:43
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 19
Author rspuzio (6075)
Entry type Definition
Classification msc 60A99
Classification msc 60G07
Synonym adapted