  Using the Riemann-Hilbert approach, we study the quasi-linear Stokes
phenomenon for the second Painlev\'e equation $y_{xx}=2y^3+xy-\alpha$. The
precise description of the exponentially small jump in the dominant solution
approaching $\alpha/x$ as $|x|\to\infty$ is given. For the asymptotic power
expansion of the dominant solution, the coefficient asymptotics is found.
