This article provides insufficient context for those unfamiliar with the subject.(July 2021) |
In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite technically, is important because it implies the stopped process is measurable. Being progressively measurable is a strictly stronger property than the notion of being an adapted process. [1] Progressively measurable processes are important in the theory of Itô integrals.
Let
The process is said to be progressively measurable [2] (or simply progressive) if, for every time , the map defined by is - measurable. This implies that is -adapted. [1]
A subset is said to be progressively measurable if the process is progressively measurable in the sense defined above, where is the indicator function of . The set of all such subsets form a sigma algebra on , denoted by , and a process is progressively measurable in the sense of the previous paragraph if, and only if, it is -measurable.
This article provides insufficient context for those unfamiliar with the subject.(July 2021) |
In mathematics, progressive measurability is a property in the theory of stochastic processes. A progressively measurable process, while defined quite technically, is important because it implies the stopped process is measurable. Being progressively measurable is a strictly stronger property than the notion of being an adapted process. [1] Progressively measurable processes are important in the theory of Itô integrals.
Let
The process is said to be progressively measurable [2] (or simply progressive) if, for every time , the map defined by is - measurable. This implies that is -adapted. [1]
A subset is said to be progressively measurable if the process is progressively measurable in the sense defined above, where is the indicator function of . The set of all such subsets form a sigma algebra on , denoted by , and a process is progressively measurable in the sense of the previous paragraph if, and only if, it is -measurable.