The random variable X is stochastically dominated by Y. Therefore, for k = 1,2,...

$\displaystyle E[X^k] < E[Y^k]$

Show

$\displaystyle \left|\frac{E[X^{k+1}]/E[X^k] }{ E[Y^{k+1}]/E[Y^k] } \right| < 1$

If needed, one can impose positivity of Y, continuity of X and Y, and/or finiteness of moments of X and Y.

Thanks in advance