I was reading a paper and the author said one can use the standard stopping time argument to show that the martingale is a square-integrable martingale. What does it mean? It is a paper talking about the solution of equation(2.1).
Condition (4.a) and the operator A is defined as below
By the assumptions of the parameters, the part surrounded by a blue square is exactly $\int_0^t Af(x(s))ds$ in (4.4). So the question is how we make out a square-integrable martingale from the assumption of merely "martingale" in the condition. I searched the "standard stopping time argument" and find one related result which construct uniformly L1 from bounded L1. Is it helpful to my situation?
Many thanks!
Maybe I should hang the link on http://www.sciencedirect.com/science/article/pii/S0304414909002166
I guess "standard stopping time argument" should be some very common and popular method like Dykin-system. But I do not know about it.