Local martingale
From Wikipedia, the free encyclopedia
In mathematics, a local martingale is a type of stochastic process, more general than a martingale.
[edit] Definition
Let 
be a probability space; let 
be a filtration of 
; let 
be an 
-adapted stochastic process taking values in the measurable space 
. Then X is called an -local martingale if there exists a sequence of stopping times ![\tau_{k} : \Omega \to [0, + \infty]](../../../math/c/7/e/c7ef289cfc994f93cea94e081ddb2205.png)
such that
- the τk are almost surely increasing:
; - the τk diverge almost surely:
; - the stopped process
is an -martingale for every k.
[edit] Reference
- Øksendal, Bernt K. (2003). Stochastic Differential Equations: An Introduction with Applications. Springer, Berlin. ISBN 3-540-04758-1.
