Decentralized energy management is of paramount importance in smart micro grids with renewables for various reasons including environmental friendliness, reduced communication overhead, and resilience to failures. In this context, the present work deals with distributed economic dispatch and demand response initiatives for grid-connected micro grids with high-penetration of wind power. To cope with the challenge of the wind's intrinsically stochastic availability, a novel energy planning approach involving the actual wind energy as well as the energy traded with the main grid, is introduced. A stochastic optimization problem is formulated to minimize the micro grid net cost, which includes conventional generation cost as well as the expected transaction cost incurred by wind uncertainty. To bypass the prohibitively high-dimensional integration involved, an efficient sample average approximation method is utilized to obtain a solver with guaranteed convergence. Leveraging the special infrastructure of the micro grid, a decentralized algorithm is further developed via the alternating direction method of multipliers. Case studies are tested to corroborate the merits of the novel approaches.