Martingale problem for superprocesses with non-classical branching functional

AbstractThe martingale problem for superprocesses with parameters (ξ,Φ,k) is studied where k(ds) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the martingale problem, an extended form of the liftings defined in [E.B. Dynkin, S.E. Kuznetsov, A.V. Skorohod, Branching measure-valued processes, Probab. Theory Related Fields 99 (1995) 55–96] exists; these liftings are part of the statement of the full martingale problem, which is hence not defined for processes X who fail to solve the partial martingale problem. The existence of a solution to the martingale problem follows essentially from Itô’s formula. The proof of uniqueness requires that we find a sequence of (ξ,Φ,kn)-superprocesses “approximating” the (ξ,Φ,k)-superprocess, where kn(ds) has the form λn(s,ξs)ds. Using an argument in [N. El Karoui, S. Roelly-Coppoletta, Propriété de martingales, explosion et représentation de Lévy–Khintchine d’une classe de processus de branchement à valeurs mesures, Stochastic Process. Appl. 38 (1991) 239–266], applied to the (ξ,Φ,kn)-superprocesses, we prove, passing to the limit, that the full martingale problem has a unique solution. This result is applied to construct superprocesses with interactions via a Dawson–Girsanov transformation

Martingale problem for (Xi, Phi, k) - superprocesses

The martingale problem for superprocesses with parameters (ξ,ɸ,k) is studied where k(ds) may not be absolutely continuous with respect to the Lebesgue measure. This requires a generalization of the concept of martingale problem: we show that for any process X which partially solves the martingale problem, an extended form of the liftings defined in [11] exists; these liftings are part of the statement of the full martingale problem, which is hence not defined for processes X who fail to solve the partial martingale problem. The existence of a solution to the martingale problem follows essentially from It{\^o}'s formula. The proof of uniqueness requires that we find a sequence of (ξ,ɸ,kn)-superprocesses "approximating" the (ξ,ɸ,k)-superprocess, where kn(ds) has the form λn (s,ξs)ds. Using an argument in [12], applied to the (ξ,ɸ,kn)-superprocesses, we derive, passing to the limit, that the full martingale problem has a unique solution. This result is apply to construct superprocesses with interactions via a Dawson-Girsanov transformation

Visibilité et prévisibilité : cartographie de la part cachée d'un paysage urbain: Etude comparée de quatre indicateurs qualifiant le champ visuel en milieu urbain

International audienceAccording to permeability theory, surroundings' configuration, and more precisely, the existence of occlusions in our enclosure may invite us to explore our environment. This article aims to analyze, in a systematic and reproducible way, the ratio of mystery in one's surrounding visualscape. To assess this property in each place, we recall three indicators relative to the boundary previsibility (entropy), the weight of visual heap (drift), and the occlusions ratio (occlusivity). We also introduce a fourth indicator which weights each occlusion (anticipation). At last, we refer to some convex partition technics of urban open spaces.Pour la théorie de la perméabilité, la configuration des lieux et plus précisément la présence d'occlusions dans notre environnement visuel immédiat, peuvent nous inciter à son exploration. L'étude présentée dans cet article a pour but d'analyser de manière systématique et reproductible la part d'inconnu, d'incertitude de l'environnement urbain immédiat d'un piéton. Pour évaluer cette propriété du visualscape en tout point, nous rappelons trois indicateurs permettant de quantifier la prévisibilité de la forme ambiante (entropie), le poids des masses visuelles (drift) et la part d'occlusions (occlusivité) avant d'en proposer un quatrième relativisant le poids de chaque occlusion (l'anticipation). Nous concluons cette analyse par une référence aux techniques de partitionnement convexe de l'espace ouvert

Longer and Heavier Vehicles for Freight Transport

The European Commission is considering to allow the use of Mega-Trucks (abbreviated as MTs in this study), vehicles measuring up to 25.25 m and weighing up to 60t, for the whole of the European Union transport system. Such trucks are already in circulation in Finland and Sweden, while several member states are considering their introduction. The analysis of the impacts of mega-trucks is quite complicated since it entails the adoption of assumptions concerning the technical characteristics of future mega-trucks, the evaluation of costs at truck level, the estimation of the repercussions on costs for the transported goods, the prediction of the market share of mega-trucks and the calculation of the external impacts, including environmental damage, accidents and wear and tear. This study collected data on the technical and economic characteristics of mega-trucks and carried out a Monte Carlo analysis in order to take the uncertainty of the main influencing factors into acount. The result was a range of potentail costs and benefits. The impacts of the introduction of mega-trucks at EU level can be positive in both economic and environmental terms. The increased payloads per vehicle are expected to reduce transport costs and lead to significant savings for operators, industry and consumers. Since fewer trucks would be required to transport the same volume of trade, the environmental and other external costs of freight transport would also be lower, even though an individual mega-truck consumes and pollutes more than a conventional truck.JRC.J.2-The economics of climate change, energy and transpor

How far is far enough? Towards an adaptive and " site-centric " modelling integrating co-visibility constraints for optimal land use

International audienceIn this article, we propose a renewed site-centric solution that allows us to characterize a specific region of interest by defining the extent of the surroundings that influence sunlight exposure. The proposed method is a mix of an adaptive refinement and a visual-based clipping technique. This method has been implemented in the SketchUp context and applied to three sites located next to the French historical thermal town of Aix-les-Bains

Longer and Heavier Vehicles: An Overview of Technical Aspects

Within the frame of the Logistics Action Plan, the European Commission is analysing the impacts of a potential introduction across the EU of Longer and Heavier Vehicles (LHVs), i.e. vehicles measuring up to 25.25 m and weighting up to 60 tons. Such vehicles are expected to improve the efficiency of the road freight sector but their impacts on the environment, infrastructure and safety need to be analysed in more depth. The present study aims at providing an overview of the technical aspects associated with LHVs with regard to energy efficiency, infrastructure (road wear and bridges) and safety issues. This is carried out at vehicle level based on a comparison with standard 40t heavy duty vehicles (HDVs). Some enhancing technologies that can potentially improve the performance of and reduce the damage caused by LHVs are described and issues that require further and detailed research are also identified.JRC.J.2-The economics of climate change, energy and transpor

Inverse radiative design in human thermal environment

International audienceThis work investigates inverse boundary design for radiative heat transfer applied to human thermal environment. The problem consists in finding the temperatures of certain surfaces in a complex configuration around the human being that satisfy both the temperature and the heat flux prescribed on his body. Such a mathematical procedure is called inverse modeling which is described by an ill-conditioned system of linear equations based on the absorption factors method. The solution is obtained by regularizing the system of equations by the Tikhonov method. As a result we obtain optimized conditions for a complex human thermal system

European Option General First Order Error Formula

We study the value of European security derivatives in the Black-Scholes model when the underlying asset ξ is approximated by random walks ξ⁽ⁿ⁾. We obtain an explicit error formula, up to a term of order O(n^{-(3/2)}), which is valid for general approximating schemes and general payoff functions. We show how this error formula can be used to find random walks ξ⁽ⁿ⁾ for which option values converge at a speed of O(n^{-(3/2)})

Arbitrarily Fast CRR Schemes

We introduce a method for the approximation of a lognormal stock price process by a Cox, Ross and Rubinstein (CRR) type of binomial scheme, which allows to reach arbitrary speed of convergence of order O(n^{-(N/2)}), for any integer N>0

Arbitrarily Fast CRR Schemes

We introduce a method for the approximation of a lognormal stock price process by a Cox, Ross and Rubinstein (CRR) type of binomial scheme, which allows to reach arbitrary speed of convergence of order O(n^{-(N/2)}), for any integer N>0