This is a question I am having related to my research. Any clarification is greatly appreciated.
A semi-martingale is defined as $M + A$, where M is a martingale and A is a process of bounded variation. So $M = M + 0$, where $A = 0$. Can we conclude that a martingale is a semi-martingale this way?
Also is it correct to say that a martingale multiplied by a process of bounded variation, (M*A) is a semi martingale. I think it is. Need some help with proving it.
Thanks in advance.