Martingale criterion (discrete time)

Theorem.

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

$E{X}_n^{-}$

or:

$E{X}_n^{+}$

Then $X$ is a martingale.

Title	Martingale criterion (discrete time)
Canonical name	MartingaleCriteriondiscreteTime
Date of creation	2013-03-22 18:34:48
Last modified on	2013-03-22 18:34:48
Owner	karstenb (16623)
Last modified by	karstenb (16623)
Numerical id	5
Author	karstenb (16623)
Entry type	Theorem
Classification	msc 60G07