Miguel Martinez

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The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the(More)
In this article we extend the exact simulation methods of Beskos et al. in [4] to the solutions of one-dimensional stochastic differential equations involving the local time of the unknown process at point zero. In order to perform the method we compute the law of the skew Brownian motion with drift. The method presented in this article covers the case(More)
In this note we propose an exact simulation algorithm for the solution of dXt = dWt + ¯ b(Xt)dt, X0 = x, (1) where ¯ b is a smooth real function except at point 0 where ¯ b(0+) = ¯ b(0−). The main idea is to sample an exact skeleton of X using an algorithm deduced from the convergence of the solutions of the skew perturbed equation dX β t = dWt + ¯ b(X β(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract In this paper we consider one-dimensional partial differential equations of parabolic type involving a divergence form operator with a discontinuous coefficient and a compatibility transmission condition. We prove existence and uniqueness result by stochastic methods which also allow us to develop a(More)
An extension of the model predictive control philosophy to the field of fuzzy control design is discussed. The main goal is to bring together the best features from both techniques. The basic idea is to divide the initial optimization problem in a set of recursive optimization subproblems or decision stages. Each subproblem is raised as a fuzzy LQR design(More)
The aim of this note is to prove estimates on mean values of the number of times that Itô processes observed at discrete times visit small balls in R d. Our technique, in the infinite horizon case, is inspired by Krylov's arguments in [2, Chap.2]. In the finite horizon case, motivated by an application in stochastic numerics, we discount the number of(More)
In 2014 and 2015, the largest Ebola virus disease (EVD) outbreak in history affected large populations across West Africa. The goal of this report is to provide an update on the epidemic and review current progress in the development, evaluation and deployment of prevention and treatment strategies for EVD. Relevant information was identified through a(More)
INTRODUCTION Monotherapy with protease-inhibitors (MPI) may be an alternative to cART for HIV treatment. We assessed the impact of this strategy on immune activation, bacterial translocation and inflammation. METHODS We performed a cross-sectional study comparing patients on successful MPI (n=40) with patients on cART (n=20). Activation, senescence,(More)
BACKGROUND AND AIMS Complete diagnostic autopsies (CDA) remain the gold standard in the determination of cause of death (CoD). However, performing CDAs in developing countries is challenging due to limited facilities and human resources, and poor acceptability. We aimed to develop and test a simplified minimally invasive autopsy (MIA) procedure involving(More)
The extent to which the Xpert MTB/RIF (Gene Xpert) contributes to tuberculosis (TB) diagnosis in samples other than sputum and cerebrospinal fluid remains uncertain. We aimed to assess the role of Xpert MTB/RIF for detecting M. tuberculosis in post-mortem tissues. We conducted a study among 30 complete diagnostic autopsies (CDA) performed at the Maputo(More)