I have a question related to stochastic little/big o notation. Consider a sequence of real-valued random variables $\{X_n\}_n$.
Is it correct $O_p(1)+X_no_p(1)=O_p(1)$ ?
Why?
I know that $O_p(1)+o_p(1)=O_p(1)$ but I'm wondering what happens if $o_p(1)$ is premultiplied by $X_n$.