1,720,972 research outputs found
MEAN FIELD GAMES MASTER EQUATIONS: FROM DISCRETE TO CONTINUOUS STATE SPACE
No full textThis paper studies the convergence of mean field games (MFGs) with finite state space to MFGs with a continuous state space. We examine a space discretization of a diffusive dynamics, which is reminiscent of the Markov chain approximation method in stochastic control, but also of finite difference numerical schemes; time remains continuous in the discretization, and the time horizon is arbitrarily long. We are mainly interested in the convergence of the solution of the associated master equations as the number of states tends to infinity. We present two approaches, to treat the case without or with common noise, both under monotonicity assumptions. The first one uses the system of characteristics of the master equation, which is the MFG system, to establish a convergence rate for the master equations without common noise and the associated optimal trajectories, both when there is a smooth solution to the limit master equation and when there is not. The second approach relies on the notion of monotone solutions introduced by [8, 9]. In the presence of common noise, we show convergence of the master equations, with a convergence rate if the limit master equation is smooth, and by compactness arguments otherwise
Industrial impact monitoring system for environmental pollution prevention and investigation
No full textCostruzione di un sistema d’analisi degli impatti territoriali dovuti alle attività industriali presenti nel comune di Rovereto (TN). Prima fase: impostazione metodologica del lavoro.
No full textDefinizione di un sistema d’analisi degli impatti territoriali dovuti alle attività industriali presenti nel comune di Rovereto (TN). Prima fase: impostazione metodologica del lavoro
No full textApproccio ecotossicologico allo sviluppo e applicazione di un sistema informativo territoriale del pericolo industriale
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A mean field model for the development of renewable capacities
Full text linkWe propose a model based on a large number of small competitive producers of renewable energies, to study the effect of subsidies on the aggregate level of capacity, taking into account a cannibalization effect. We first derive a model to explain how long-time equilibrium can be reached on the market of production of renewable electricity and compare this equilibrium to the case of monopoly. Then we consider the case in which other capacities of production adjust to the production of renewable energies. The analysis is based on a master equation and we get explicit formulae for the long-time equilibria. We also provide new numerical methods to simulate the master equation and the evolution of the capacities. Thus we find the optimal subsidies to be given by a central planner to the installation and the production in order to reach a desired equilibrium capacity
Dabase project for environmentl impact evaluation of productive activities in a densiily populated area
No full textWEP/19
Finite state mean field games with Wright–Fisher common noise
No full textWe force uniqueness in finite state mean field games by adding a Wright–Fisher common noise. We achieve this by analyzing the master equation of this game, which is a degenerate parabolic second-order partial differential equation set on the simplex whose characteristics solve the stochastic forward-backward system associated with the mean field game; see Cardaliaguet et al. [10]. We show that this equation, which is a non-linear version of the Kimura type equation studied in Epstein and Mazzeo [28], has a unique smooth solution whenever the normal component of the drift at the boundary is strong enough. Among others, this requires a priori estimates of Hölder type for the corresponding Kimura operator when the drift therein is merely continuous
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