On the splitting-up method for rough (partial) differential equations

This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to stochastic partial differential equations arising in control theory and nonlinear filtering are given

An Overview of Integral Quadratic Constraints for Delayed Nonlinear and Parameter-Varying Systems

A general framework is presented for analyzing the stability and performance of nonlinear and linear parameter varying (LPV) time delayed systems. First, the input/output behavior of the time delay operator is bounded in the frequency domain by integral quadratic constraints (IQCs). A constant delay is a linear, time-invariant system and this leads to a simple, intuitive interpretation for these frequency domain constraints. This simple interpretation is used to derive new IQCs for both constant and varying delays. Second, the performance of nonlinear and LPV delayed systems is bounded using dissipation inequalities that incorporate IQCs. This step makes use of recent results that show, under mild technical conditions, that an IQC has an equivalent representation as a finite-horizon time-domain constraint. Numerical examples are provided to demonstrate the effectiveness of the method for both class of systems

A generalized Fernique theorem and applications

We prove a generalisation of Fernique's theorem which applies to a class of (measurable) functionals on abstract Wiener spaces by using the isoperimetric inequality. Our motivation comes from rough path theory where one deals with iterated integrals of Gaussian processes (which are generically not Gaussian). Gaussian integrability with explicitly given constants for variation and H\"older norms of the (fractional) Brownian rough path, Gaussian rough paths and the Banach space valued Wiener process enhanced with its L\'evy area [Ledoux, Lyons, Quian. "L\'evy area of Wiener processes in Banach spaces". Ann. Probab., 30(2):546--578, 2002] then all follow from applying our main theorem.Comment: To be published in the Proceedings of the AMS

Intra- and Inter-Industry Productivity Spillovers in OECD Manufacturing: A Spatial Econometric Perspective

We adopt a spatial econometric approach to estimate intra- and inter-industry productivity spillovers in total factor productivity transmitted through input-output relations in a sample of 13 OECD countries and 15 manufacturing industries. Both R&D spillovers as well as remainder, input-output-related linkage effects are accounted for, the latter of which we model by a spatial regressive error process. We find that knowledge spillovers occur both horizontally and vertically, whereas remainder spillovers are primarily of intra-industry type. Notably, these intra-industry remainder spillovers turn out economically more significant than R&D spillovers.intra-industry spillovers, inter-industry spillovers, productivity, spatial econometrics, research and development

GM Estimation of Higher Order Spatial Autoregressive Processes in Panel Data Error Component Models

This paper presents a generalized moments (GM) approach to estimating an R-th order spatial regressive process in a panel data error component model. We derive moment conditions to estimate the parameters of the higher order spatial regressive process and the optimal weighting matrix required to achieve asymptotic efficiency. We prove consistency of the proposed GM estimator and provide Monte Carlo evidence that it performs well also in reasonably small samples.spatial models, panel data models, error component models

Estimation of Higher-Order Spatial Autoregressive Panel Data Error Component Models

This paper develops an estimator for higher-order spatial autoregressive panel data error component models with spatial autoregressive disturbances, SARAR(R,S). We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define a generalized two-stages least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their joint asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.higher-order spatial dependence, generalized moments estimation, two-stages least squares, asymptotic statistics