Rough path recursions and diffusion approximations

In this article, we consider diffusion approximations for a general class of stochastic recursions. Such recursions arise as models for population growth, genetics, financial securities, multiplicative time series, numerical schemes and MCMC algorithms. We make no particular probabilistic assumptions on the type of noise appearing in these recursions. Thus, our technique is well suited to recursions where the noise sequence is not a semi-martingale, even though the limiting noise may be. Our main theorem assumes a weak limit theorem on the noise process appearing in the random recursions and lifts it to diffusion approximation for the recursion itself. To achieve this, we approximate the recursion (pathwise) by the solution to a stochastic equation driven by piecewise smooth paths; this can be thought of as a pathwise version of backward error analysis for SDEs. We then identify the limit of this stochastic equation, and hence the original recursion, using tools from rough path theory. We provide several examples of diffusion approximations, both new and old, to illustrate this technique.Comment: Published at http://dx.doi.org/10.1214/15-AAP1096 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Censorship challenges to books in Scottish public libraries

Censorship challenges to books in UK public libraries have received renewed attention recently. This study sought to establish the incidence of censorship challenges to books in Scottish public libraries in the years 2005-2009 and the actions taken in response to these challenges. It was found that eight local authorities in Scotland had received formal censorship challenges to books, with a total of 15 challenges throughout the country. The most common action taken in response to these challenges was for the book to be kept in stock in its original position with the rationale for this explained to the complainer, with the second most common action being taken to move the title to another section of the library. Two books were removed from the library in response to a censorship challenge. The largest numbers of challenges were made against books on the basis of sexual material

Stochastic PDEs with multiscale structure

We study the spatial homogenisation of parabolic linear stochastic PDEs exhibiting a two-scale structure both at the level of the linear operator and at the level of the Gaussian driving noise. We show that in some cases, in particular when the forcing is given by space-time white noise, it may happen that the homogenised SPDE is not what one would expect from existing results for PDEs with more regular forcing terms

Deterministic homogenization for fast-slow systems with chaotic noise

Consider a fast-slow system of ordinary differential equations of the form $\dot x=a(x,y)+\varepsilon^{-1}b(x,y)$, $\dot y=\varepsilon^{-2}g(y)$, where it is assumed that $b$ averages to zero under the fast flow generated by $g$. We give conditions under which solutions $x$ to the slow equations converge weakly to an It\^o diffusion $X$ as $\varepsilon\to0$. The drift and diffusion coefficients of the limiting stochastic differential equation satisfied by $X$ are given explicitly. Our theory applies when the fast flow is Anosov or Axiom A, as well as to a large class of nonuniformly hyperbolic fast flows (including the one defined by the well-known Lorenz equations), and our main results do not require any mixing assumptions on the fast flow.Comment: 31 page

Subsidies to Industry and the Environment

Governments support particular firms or sectors by granting low interest financing, reduced regulation, tax relief, price supports, monopoly rights, and a variety of other subsidies. Previous work in partial equilibrium shows that subsidies to environmentally sensitive industries increases output and pollution emissions. We examine the environmental effects of subsidies in general equilibrium. Since all resources are used, whether or not subsidies increase emissions depends on the relative emissions intensity and incentives to emit of the subsidized industry versus the emissions intensity and the incentives to emit of the industry which would otherwise use the resources. Since subsidies must move resources to a less productive use, the economy wide marginal product of emissions falls with an increase in any subsidy, tending to decrease emissions. On the other hand, subsidies tend to move resources to more emissions intensive industries. Thus, subsidies increase pollution emissions if resources are moved to an industry for which emissions intensity is high enough to overcome the reduction in emissions caused by lower overall marginal product of emissions. We show that, under general conditions, subsidies also increase the interest rate, thus causing the economy to over-accumulate capital. Steady state emissions then rise, even if emissions fall in the short run. We also derive an optimal second best environmental policy given industrial subsidies. The results indicate that, under reasonable conditions, subsidies raise the opportunity cost of environmental quality in the long run. Finally, we examine the relationship between growth and the environment with subsidies. Under more restrictive conditions, reducing some subsidies may offer a path to sustainable development by raising income and at the same time improving the environment.Subsidies, pork, price supports, output subsidies, input subsidies, pollution, emissions.

Libet and Freedom in a Mind-Haunted World

Saigle, Dubljevic, and Racine (2018) claim that Libet-style experiments are insufficient to challenge that agents have free will. They support this with evidence from experimen- tal psychology that the folk concept of freedom is consis- tent with monism, that our minds are identical to our brains. However, recent literature suggests that evidence from experimental psychology is less than determinate in this regard, and that folk intuitions are too unrefined as to provide guidance on metaphysical issues like monism. In light of this, it is worthwhile to examine the authors’ insuf- ficiency claim under the assumption that monism is false and dualism true (our minds are not identical to our brains). We conclude that, were dualism true, then Libet- style experiments would tell us no more about freedom and moral responsibility than what the authors initially claimed, thus further bolstering their point that Libet-style experiments are ill-suited to speak to the free will of agents. In what follows we first discuss some of the reasons to be skeptical of using folk intuitions to make claims about the nature of freedom and moral responsibility. We then draw from the work of E. J. Lowe to demonstrate that Libet-style experiments would likely give the same results regardless of the truth of monism or dualism

Proposed Bond Funded Capital Spending

The Governor has proposed to issue $1,347,250,000 in bonds in order to finance spending on road construction, school buildings, and other construction projects. This note estimates the effect of this capital spending program on the Georgia economy

Free trade agreements and the environment with pre-existing subsidies

Countries that wish to erect trade barriers have a variety of instruments at their disposal. In addition to tariffs and quotas, countries can offer tax relief, low interest financing, reduced regulation ,and other subsidies to domestic industries facing foreign competition. In a trade agreement, countries typically agree to reduce not only tariffs, but also subsidies. We consider the effect of a trade agreement on pollution emissions. We show that while reducing tariffs may indeed increase pollution intensive production in a country, reductions in some subsidies required by the trade agreement reduce pollution in general equilibrium for reasonable parameter values. The reduction results from two effects. First, a reduction in subsidies to firms reduces pollution-causing capital accumulation. Second, if subsidized firms, industries, and/or state owned enterprises are sufficiently more pollution intensive, then reducing subsidies moves capital and labor from more to less pollution intensive firms. We calibrate the model to the case of China and show that pollution emissions after China's accession to the WTO are up to 22.9 percent lower than a baseline in which China does not enter the WTO, without any pollution abatement policy changes or environmental side agreements.trade agreements, domestic subsidies, pollution emissions, dynamic general equilibrium