# Is it possibile to use Ito Formula here?

I have this process: $$dY_s^y=\alpha(s,Y_s^y)ds + \frac{1}{2}\beta^2(Y_s^y)^2dW_s$$ with inital value $$Y_s^y=y$$. Moreover $$\alpha(s,y)$$ is a linear function in $$y$$ and bounded is $$s$$. I was wondering if it would be possibile to apply Ito Lemma to prove that for $$y \to +\infty$$ the process goes to $$+\infty$$? Or is it possible in some way to prove that the process goes to $$+\infty$$ or that it is grater then a constant $$K$$? Thanks for help.

• I think you should state more clearly what you mean that the "process" goes to infinity when the initial value goes to infinity. Dec 20 '20 at 18:52
• @fesman Actually I want it bo greater then a constant, could it be possible? Dec 20 '20 at 22:21