A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Making Young Voters: The Impact of Preregistration on Youth Turnout

© 2016 by the Midwest Political Science Association.Recent research has cast doubt on the potential for various electoral reforms to increase voter turnout. In this article, we examine the effectiveness of preregistration laws, which allow young citizens to register before being eligible to vote. We use two empirical approaches to evaluate the impact of preregistration on youth turnout. First, we implement difference-in-difference and lag models to bracket the causal effect of preregistration implementation using the 2000-2012 Current Population Survey. Second, focusing on the state of Florida, we leverage a discontinuity based on date of birth to estimate the effect of increased preregistration exposure on the turnout of young registrants. In both approaches, we find preregistration increases voter turnout, with equal effectiveness for various subgroups in the electorate. More broadly, observed patterns suggest that campaign context and supporting institutions may help to determine when and if electoral reforms are effective.