Levy martingale characterization

Theorem (Levy’s martingale characterisation).

Let W(t),t0, be a stochastic processMathworldPlanetmath and let Ft=σ(Ws,st) be the filtrationPlanetmathPlanetmath generated by it. Then W(t) is a Wiener processMathworldPlanetmath if and only if the following conditions hold:

  1. 1.

    W(0)=0 almost surely;

  2. 2.

    The sample paths tW(t) are continuous almost surely;

  3. 3.

    W(t) is a martingaleMathworldPlanetmath with respect to the filtration t;

  4. 4.

    |W(t)|2-t is a martingale with respect to t.

Title Levy martingale characterization
Canonical name LevyMartingaleCharacterization
Date of creation 2013-03-22 15:12:48
Last modified on 2013-03-22 15:12:48
Owner skubeedooo (5401)
Last modified by skubeedooo (5401)
Numerical id 5
Author skubeedooo (5401)
Entry type Theorem
Classification msc 60J65