A novel type of Sobolev-Poincar\'e inequality for submanifolds of Euclidean space

For functions on generalised connected surfaces (of any dimensions) with boundary and mean curvature, we establish an oscillation estimate in which the mean curvature enters in a novel way. As application we prove an a priori estimate of the geodesic diameter of compact connected smooth immersions in terms of their boundary data and mean curvature. These results are developed in the framework of varifolds. For this purpose, we establish that the notion of indecomposability is the appropriate substitute for connectedness and that it has a strong regularising effect; we thus obtain a new natural class of varifolds to study. Finally, our development leads to a variety of questions that are of substance both in the smooth and the nonsmooth setting.Comment: 35 pages, no figure

An isoperimetric inequality for diffused surfaces

For general varifolds in Euclidean space, we prove an isoperimetric inequality, adapt the basic theory of generalised weakly differentiable functions, and obtain several Sobolev type inequalities. We thereby intend to facilitate the use of varifold theory in the study of diffused surfaces.Comment: Awaiting publication in Kodai Math. J. The final printed version will be different. 14 pages, no figure

A Functional Limit Theorem for Limit Order Books with State Dependent Price Dynamics

We consider a stochastic model for the dynamics of the two-sided limit order book (LOB). Our model is flexible enough to allow for a dependence of the price dynamics on volumes. For the joint dynamics of best bid and ask prices and the standing buy and sell volume densities, we derive a functional limit theorem, which states that our LOB model converges in distribution to a fully coupled SDE-SPDE system when the order arrival rates tend to infinity and the impact of an individual order arrival on the book as well as the tick size tends to zero. The SDE describes the bid/ask price dynamics while the SPDE describes the volume dynamics.Comment: 43 page

Do Magazines' "Companion Websites" Cannibalize the Demand for the Print Version?

We analyze the relationship between website visits, magazine demand and the demand for advertising pages using Granger non-causality tests on the basis of an extensive and externally audited quarterly data set for the German magazine market spanning the period I/1998 to II/2004. We use traditional panel data estimators and an estimator suitable for heterogeneity across magazines. We find very robust evidence for positive effects from website visits to circulation. There is no evidence of causality running in the opposite direction. Our findings are contrary to the widespread belief that the Internet will cannibalize print media markets.Granger causality; heterogeneous panel data models; Mean Group Estimation; website visits; magazine circulation

Do Magazines' ”Companion Websites” Cannibalize the Demand for the Print Version?

We analyze the extent to which visits to a magazine's companion website affects total circulation, subscription, kiosk sales and foreign sales using Granger causality tests on the basis of monthly data for the German magazine market spanning the period January 1998 to September 2005. We find evidence for positive effects of website visits on magazine subscription but negative effects on magazine kiosk sales. Contrary to the widespread belief that the Internet will cannibalize print media markets, our results do not, however, provide evidence for website visits adversely affecting total circulation.Granger causality; heterogeneous panel data models; Mean Group Estimation; website visits; magazine circulation

True versus spurious state dependence in firm performance: the case of West German exports

This paper analyzes the persistence of firms’ exporting behavior in a panel of West German manufacturing firms. Dynamic binary choice models allow us to distinguish between true and spurious state dependence in firm performance. Using random effects models as well as a recent fixed effect approach which imposes few restrictions on unobservables, we find robust evidence of state dependence in the current export status of firms. Unobserved permanent firm heterogeneity (“spurious state dependence”) is found to be less important than suggested by earlier studies. The existence of true state dependence in exports has direct economic policy implications: if policy successfully turns non-exporters into exporters, the effect is likely to be lasting.state dependence; export activity; dynamic binary choice models

Do Magazines' "Companion Websites" Cannibalize the Demand for the Print Version?

We analyze the relationship between website visits, magazine demand and the demand for advertising pages using Granger non-causality tests on the ba- sis of an extensive and externally audited quarterly data set for the German magazine market spanning the period I/1998 to II/2004. We use traditional panel data estimators and an estimator suitable for heterogeneity across mag- azines. We find very robust evidence for positive effects from website visits to circulation. There is no evidence of causality running in the opposite direction. Our findings are contrary to the widespread belief that the Internet will cannibalize print media markets. --Granger causality,heterogeneous panel data models,Mean Group Estimation,website visits,magazine circulation