semimartingale
Sign in to saveIn probability theory, a real-valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and a càdlàg adapted finite-variation process. Semimartingales are "good integrators", forming the largest class of processes with respect to which the Itô integral and the Stratonovich integral can be defined.
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Encyclopedic overview
14 sectionsContents
- Definition
- Alternative definition
- Examples
- Properties
- Semimartingale decompositions
- Continuous semimartingales
- Special semimartingales{{Anchor|Special semimartingale}}
- Multiplicative decompositions
- Purely discontinuous semimartingales / quadratic pure-jump semimartingales
- Continuous-time and discrete-time components of a semimartingale
- Canonical Decomposition
- Semimartingales on a manifold
- See also
- References
In probability theory, a real-valued stochastic process X is called a semimartingale if it can be decomposed as the sum of a local martingale and a càdlàg adapted finite-variation process. Semimartingales are "good integrators", forming the largest class of processes with respect to which the Itô integral and the Stratonovich integral can be defined.
The class of semimartingales is quite large (including, for example, all continuously differentiable processes, Brownian motion and Poisson processes). Submartingales and supermartingales together represent a subset of the semimartingales.
Excerpted from Wikipedia’s “semimartingale” article, available under the CC BY-SA 4.0 licence.