Particle approximation for Lagrangian Stochastic Models with specular boundary condition

In this paper, we prove a particle approximation, in the sense of the propagation of chaos, of a Lagrangian stochastic model submitted to specular boundary condition and satisfying the mean no-permeability condition

Clarification and complement to "Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons"

In this note, we clarify the well-posedness of the limit equations to the mean-field $N$-neuron models proposed in Baladron et al. and we prove the associated propagation of chaos property. We also complete the modeling issue in Baladron et al. by discussing the well-posedness of the stochastic differential equations which govern the behavior of the ion channels and the amount of available neurotransmitters

Nash equilibrium for coupling of CO2 allowances and electricity markets

In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a clear Nash equilibrium that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions covered

Game theory analysis for carbon auction market through electricity market coupling

In this paper, we analyze Nash equilibria between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a clear Nash equilibrium on the power market that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions released.Comment: arXiv admin note: text overlap with arXiv:1311.153

On the ε\varepsilon-Euler-Maruyama scheme for time inhomogeneous jump-driven SDEs

We consider a class of general SDEs with a jump integral term driven by a time-inhomogeneous random Poisson measure. We propose a two-parameters Euler-type scheme for this SDE class and prove an optimal rate for the strong convergence with respect to the $L^p(\Omega)$-norm and for the weak convergence. One of the primary issues to address in this context is the approximation of the noise structure when it can no longer be expressed as the increment of random variables. We extend the Asmussen-Rosinski approach to the case of a fully dependent jump coefficient and time-dependent Poisson compensation, handling contribution of jumps smaller than $\varepsilon$ with an appropriate Gaussian substitute and exact simulation for the large jumps contribution. For any $p \geq 2$, under hypotheses required to control the $L^p$-moments of the process, we obtain a strong convergence rate of order $1/p$. Under standard regularity hypotheses on the coefficients, we obtain a weak convergence rate of $1/n+\epsilon^{3-\beta}$, where $\beta$ is the Blumenthal-Getoor index of the underlying L\'evy measure. We compare this scheme with the Rubenthaler's approach where the jumps smaller than $\varepsilon$ are neglected, providing strong and weak rates of convergence in that case too. The theoretical rates are confirmed by numerical experiments afterwards. We apply this model class for some anomalous diffusion model related to the dynamics of rigid fibres in turbulence

Modeling the wind circulation around mills with a Lagrangian stochastic approach

This work aims at introducing model methodology and numerical studies related to a Lagrangian stochastic approach applied to the computation of the wind circulation around mills. We adapt the Lagrangian stochastic downscaling method that we have introduced in [3] and [4] to the atmospheric boundary layer and we introduce here a Lagrangian version of the actuator disc methods to take account of the mills. We present our numerical method and numerical experiments in the case of non rotating and rotating actuator disc models. We also present some features of our numerical method, in particular the computation of the probability distribution of the wind in the wake zone, as a byproduct of the fluid particle model and the associated PDF method

Optimal Rate of Convergence of a Stochastic Particle Method to Solutions of 1D Viscous Scalar Conservation Law Equations

The aim of this work is to present the analysis of the rate of convergence of a stochastic particle method for 1D viscous scalar conservation law equations. The convergence rate result is \mathcal O(\D t + 1/\sqrt{N}), where $N$ is the number of numerical particles and \D t is the time step of the first order Euler scheme applied to the dynamic of the interacting particles

Analyzing the Applicability of Random Forest-Based Models for the Forecast of Run-of-River Hydropower Generation

ABSTRACT: Analyzing the impact of climate variables into the operational planning processes is essential for the robust implementation of a sustainable power system. This paper deals with the modeling of the run-of-river hydropower production based on climate variables on the European scale. A better understanding of future run-of-river generation patterns has important implications for power systems with increasing shares of solar and wind power. Run-of-river plants are less intermittent than solar or wind but also less dispatchable than dams with storage capacity. However, translating time series of climate data (precipitation and air temperature) into time series of run-of-river-based hydropower generation is not an easy task as it is necessary to capture the complex relationship between the availability of water and the generation of electricity. This task is also more complex when performed for a large interconnected area. In this work, a model is built for several European countries by using machine learning techniques. In particular, we compare the accuracy of models based on the Random Forest algorithm and show that a more accurate model is obtained when a finer spatial resolution of climate data is introduced. We then discuss the practical applicability of a machine learning model for the medium term forecasts and show that some very context specific but influential events are hard to capture.info:eu-repo/semantics/publishedVersio