Cost Heterogeneity and the Potential Savings from Market-Based Policies

Policy makers and analysts are often faced with situations where it is unclear whether market-based instruments hold real promise of reducing costs, relative to conventional uniform standards. We develop analytic expressions that can be employed with modest amounts of information to estimate the potential cost savings associated with market-based policies, with an application to the environmental policy realm. These simple formulae can identify instruments that merit more detailed investigation. We illustrate the use of these results with an application to nitrogen oxides control by electric utilities in the United States.

Stochastic switching in infinite dimensions with applications to random parabolic PDE

© 2015 Society for Industrial and Applied Mathematics.We consider parabolic PDEs with randomly switching boundary conditions. In order to analyze these random PDEs, we consider more general stochastic hybrid systems and prove convergence to, and properties of, a stationary distribution. Applying these general results to the heat equation with randomly switching boundary conditions, we find explicit formulae for various statistics of the solution and obtain almost sure results about its regularity and structure. These results are of particular interest for biological applications as well as for their significant departure from behavior seen in PDEs forced by disparate Gaussian noise. Our general results also have applications to other types of stochastic hybrid systems, such as ODEs with randomly switching right-hand sides.