Lyapunov stabilizability of controlled diffusions via a superoptimality principle for viscosity solutions

We prove optimality principles for semicontinuous bounded viscosity solutions of Hamilton-Jacobi-Bellman equations. In particular we provide a representation formula for viscosity supersolutions as value functions of suitable obstacle control problems. This result is applied to extend the Lyapunov direct method for stability to controlled Ito stochastic differential equations. We define the appropriate concept of Lyapunov function to study the stochastic open loop stabilizability in probability and the local and global asymptotic stabilizability (or asymptotic controllability). Finally we illustrate the theory with some examples.Comment: 22 page

The kinematics of molecular clumps surrounding hot cores in G29.96-0.02 and G31.41+0.31

We present high angular resolution interferometric observations of the 3 and 1.3mm continuum emission, and HCO+(1-0) and SiO(2-1)v=0 lines, obtained with the Owens Valley Radio Observatory millimeter-wave array, toward two hot cores (HCs) associated with two well known ultracompact (UC) HII regions: G29.96-0.02 and G31.41+0.31. These HCs are believed to host young forming massive stars which have been suggested to be surrounded by massive rotating accretion disks. The aim of these new observations is to study the structure and kinematics of the molecular clumps surrounding the HCs and nearby UCHII regions at moderately high angular resolution. Our observations reveal that the clumps within which the HCs and UCHII regions are embedded have a complex kinematical structure. The total mass of the clumps is estimated to be in the range 1000-3000 Msun, consistent with previous findings. Our observations also show compelling evidence that the clump in G29.96-0.02 is contracting onto the HC position, suggesting that the accretion process onto the massive young stellar object embedded in the HC is still ongoing. In these objects the kinematical structure that we observe is also compatible with the presence of a massive rotating disk within the HC, even though we cannot prove this suggestion with our data. The case of G31.41+0.31 is more complicated, and our data, although consistent with the presence of an inner disk and an infalling envelope around it, do not have the required spatial resolution to resolve the different structures.Comment: 13 pages, 15 figs, A&A in pres

Estimating potential output using business survey data in a svar framework

Potential output and the related concept of output gap play a central role in the macroeconomic policy interventions and evaluations. In particular, the output gap, defined as the difference between actual and potential output, conveys useful information on the cyclical position of a given economy. This paper proposes estimates of the Italian potential output based on a structural VAR model using data coming from business surveys. This kind of data, given their cyclical profile, are particularly useful for detrending purposes, as they allow to include information concerning the business cycle activity. The ability of the cyclical GDP component obtained with the SVAR decomposition to forecast inflation and to detect business cycle turning points over the expansion and recession phases is then performed.output gap, business survey data, structural VAR models, forecast ability

Estimating potential output using business survey data in a SVAR framework

Potential output and the related concept of output gap play a central role in the macroeconomic policy interventions and evaluations. In particular, the output gap, defined as the difference between actual and potential output, conveys useful information on the cyclical position of a given economy. The aim of this paper is to propose estimates of the Italian potential GDP based on structural VAR models. With respect to other techniques, like the univariate filters (i.e. the Hodrick-Prescott filter), the estimates obtained through the SVAR methodology are free from end-of-sample problems, thus resulting particularly useful for short-term analysis. In order to provide information on the economic fluctuations, data coming from business surveys are considered in the model. This kind of data, given their cyclical profile, are particularly useful for detrending purposes, as they allow to include information concerning the business cycle activity. To assess the estimate reliability, an end-of-sample revision evaluation is performed. The ability of the cyclical GDP component to detect business cycle turning points is then performed by comparing the estimated output gaps, extracted with different detrending methods, over the expansion and recession phases of the Italian business cycle chronology.potential output, business survey data, structural VAR models, end-of-sample revisions.

Technology Strategies in the Knowldge Economy. The Licensing Activity of Himont

The exchange of technologies and technological knowledge - through joint-ventures, partnerships, licensing, cross-licensing, R&D contracts - and the upsurge of markets for technology are main features of the "knowledge-based" economy. Competitive strengths are shifting from technological aspects to different levels of competitive behaviour, and companies are gradually changing their aptitude towards technology trading and exchange. The aim of this paper is to discuss the extent of technology licensing in chemicals, and specifically of one large firm - Himont - widely involved in licensing its process technologies. By analysing this case study, this paper explores the motivations for technology licensing, the managerial solutions that Himont adopted for licensing its technologies, and the implications of this strategy in terms of antitrust policy. One of the main result emerging from the analysis is the role of external technology suppliers. By increasing the potential competition in the product market, they create incentives for incumbent firms to license-out their technologies, and earn profits in the market for technology.Corporate Strategies, Technology Licensing, Chemical Industry, Division of Innovative Labour, Markets for Technology, Antitrust Policy.

Contestability and collateral in credit markets with adverse selection

The work discusses a basic proposition in the theory of competition in markets with adverse selection (Bester, 1985). By working out the sequence of market transactions, we show that the effectiveness of collateral in avoiding equilibrium rationing depends on an assumption of uncontestability of the loan market. If contestability is restored to its proper place, the separation of borrower by means of sufficient collateral does not impede the emergence of credit rationing, which results from a coordination failure among risk-neutral banks. As a consequence, even in a risk-neutral environment with suitable endowments, the use of collateral in credit contracts could not be a socially efficient screening-device. Our conclusion on rationing does not stand in contrast with the general result of Gale (1996).Adverse selection; Collateral; Rationing; Contestable markets;

The isoperimetric problem for nonlocal perimeters

We consider a class of nonlocal generalized perimeters which includes fractional perimeters and Riesz type potentials. We prove a general isoperimetric inequality for such functionals, and we discuss some applications. In particular we prove existence of an isoperimetric profile, under suitable assumptions on the interaction kernel.Comment: 17 p

Convergence of nonlocal geometric flows to anisotropic mean curvature motion

We consider nonlocal curvature functionals associated with positive interaction kernels, and we show that local anisotropic mean curvature functionals can be retrieved in a blow-up limit from them. As a consequence, we prove that the viscosity solutions to the rescaled nonlocal geometric flows locally uniformly converge to the viscosity solution to the anisotropic mean curvature motion. The result is achieved by combining a compactness argument and a set-theoretic approach related to the theory of De Giorgi's barriers for evolution equations.Comment: 19 page

Volume constrained minimizers of the fractional perimeter with a potential energy

We consider volume-constrained minimizers of the fractional perimeter with the addition of a potential energy in the form of a volume inte- gral. Such minimizers are solutions of the prescribed fractional curvature problem. We prove existence and regularity of minimizers under suitable assumptions on the potential energy, which cover the periodic case. In the small volume regime we show that minimizers are close to balls, with a quantitative estimate