A quasimartingale is a concept from stochastic processes and refers to a stochastic process that has finite mean variation. Quasimartingales are generalizing semimartingales in the sense as they do not have to be càdlàg, and they are exactly semimartingales if they are càdlàg. Quasimartingales were introduced by the American mathematician Donald Fisk in 1965.
Some authors use the term as a synonym for semimartingale and assume the process is càdlàg.
Quasimartingale.
Let formula_1 be a filtred probability space and let formula_2 be a partition of the interval formula_3. Further, let formula_4 be an adapted stochastic process. The "(mean) variation of formula_5" is defined as
formula_6
The process formula_5 is a quasimartingale if formula_8 for all formula_9 and the process has finite variation:
formula_10