Abstract

‎‎‎We introduce near-martingales in the setting of quantum probability spaces and present a trick for investigating some of their properties‎. ‎For instance‎, ‎we give a near-martingale analogous result of the fact that the space of all bounded $L^p$-martingales‎, ‎equipped with the norm $\|\cdot\|_p$‎, ‎is isometric to $L^p(\mathfrak{M})$ for $p>1$‎. ‎We also present Doob and Riesz decompositions for the near-submartingale and provide Gundy's decomposition for $L^1$-bounded near-martingales‎. ‎In addition‎, ‎the interrelation between near-martingales and the instantly independence is studied‎.

Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call