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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.

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

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