Suppose $X$ and $Y$ are two random variables where $X$ SOSD* $Y$. Let $g(\bullet)$ be a monotonic function and $X'=g(X)$ and $Y'=g(Y)$. Under what conditions of $g$ is
$X'$ SOSD $Y'$?
I know if $g$ is linear, SOSD property is reserved. Is there any suff and nec conditions of $g$ that assures SOSD property ?
*second-order stochastic dominance.