Probability theory and stochastic processes Martingales Concept
Submartingale
Summary
A submartingale is an adapted, integrable stochastic process whose conditional expectation of a future value, given the present information, is at least the present value. It models the fortune in a game that is favourable or fair to the player. Every martingale is a submartingale, and convex functions of martingales give many more examples. Doob's inequalities and convergence theorems are proved for submartingales.
Further reading
About this page
| Tag | 6M852B4RA8 |
|---|---|
| URI | m2://6M852B4RA8 |
| Kind | concept |
| Writing | W0 stub |
| MSC | 60G42, 60G44 |
| Specializes | Stochastic process |
| Changed | 2 November 2026 |
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Results about this
- Doob's upcrossing inequality
- Doob's martingale inequality
- Doob's martingale convergence theorems
- Doob–Meyer decomposition theorem
- Doob decomposition theorem