We consider the approximation by multidimensional finite volume schemes of the transport of an initial measure by a Lipschitz flow. We first consider a scheme defined via characteristics, and we prove the convergence to the continuous solution, as the time-step and the ratio of the space step to the time-step tend to zero. We then consider a second finite volume scheme, obtained from the first ...

We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove...

We introduce and study a class of infinite-horizon non-zero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove...

We analyze a finite volume scheme for nonlocal SIR model, which is a nonlocal reaction-diffusion system modeling an epidemic disease. We establish existence solutions to the finite volume scheme, and show that it converges to a weak solution. The convergence proof is based on deriving series of a priori estimates and using a general L compactness criterion.

An arbitrary order differentiator that, in the absence of noise, converges to the true derivatives of the signal after a finite time independent of the initial differentiator error is presented. The only assumption on a signal to be differentiated (n−1)-times is that its n-th derivative is uniformly bounded by a known constant. The proposed differentiator switches from a newly designed uniform ...

In this paper, we consider a critically loaded G/M/1 queue and contrast its transient behaviour with the transient behaviour of stable (or unstable) G/M/1 queues. We show that the departure process from a critical G/M/1 queue converges weakly to a Poisson process. However, as opposed to the stable (or unstable) case, we show that the departure process of a critical GI/M/I queue does not couple ...

Extremum-seeking control is a class of methods where real-time static optimization of a dynamic system is achieved by controlling the gradient. Estimation of the gradient is a key issue in extremum-seeking methods. In multi-unit optimization, the gradient is obtained using finite difference of the outputs of multiple identical units driven with inputs that are offset by a design parameter. Howe...

We study the behavior of solutions to a Schrödinger equation with large, rapidly oscillating, mean zero, random potential with Gaussian distribution. We show that in high dimension d > m, where m is the order of the spatial pseudo-differential operator in the Schrödinger equation (with m = 2 for the standard Laplace operator), the solution converges in the L sense uniformly in time over finite ...

We present a stabilized finite element method for the Hu-Washizu formulation of linear elasticity based on simplicial meshes leading to the stabilized nodal strain formulation or node-based uniform strain elements. We show that the finite element approximation converges uniformly to the exact solution for the nearly incompressible case.

On the optimality of universal classifiers for finite-length individual test sequences. Abstract It has been demonstrated that if two individual sequences are independent realizations of two finite-order, finite alphabet, stationary Markov processes, an empirical divergence measure (ZMM) that is based on cross-parsing of one sequence relative to the second one converges to the relative entropy ...