Probability theory and stochastic processes Stochastic processes: general theory Concept
Adapted process
Summary
A stochastic process is adapted to a filtration when its value at each time is determined by the information available at that time. Adapted processes cannot see the future. Adaptedness is part of the definition of a martingale and of the stochastic integral, where the integrand must not anticipate the noise.
Where this leads
18 pages build on this one.
- Doob's upcrossing inequality
- Doob's martingale inequality
- Lévy's characterization of Brownian motion
- Optional stopping theorem
- Submartingale
- Tanaka's formula
- Supermartingale
- Doob's martingale convergence theorems
- Semimartingale
- Itô calculus
- Stopped process
- Burkholder–Davis–Gundy inequality
- Doob–Meyer decomposition theorem
- Skorokhod's embedding theorem
- Stochastic differential equation
- Doob decomposition theorem
- Girsanov theorem
- Local martingale
Further reading
About this page
| Tag | YRNFE016FF |
|---|---|
| URI | m2://YRNFE016FF |
| Kind | concept |
| Writing | W0 stub |
| MSC | 60G05, 60G07 |
| Specializes | Stochastic process |
| Same as | |
| Changed | 2 November 2026 |
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