Martingale criterion (discrete time)

Theorem.

Let $X=(X_{n},\mathcal{F}_{n})$ be a local martingale. If there is an $n_{0}\in\mathbb{N}$ such that $\forall\ n\geq n_{0},n\in\mathbb{N}$ either:

 $\displaystyle EX_{n}^{-}$ $\displaystyle<\infty$

or:

 $\displaystyle EX_{n}^{+}$ $\displaystyle<\infty$

Then $X$ is a martingale.

Title Martingale criterion (discrete time) MartingaleCriteriondiscreteTime 2013-03-22 18:34:48 2013-03-22 18:34:48 karstenb (16623) karstenb (16623) 5 karstenb (16623) Theorem msc 60G07