arXiv subjects

Hector Olivero

Publications and source records attributed to Hector Olivero.

3 recordsLinked to original sources

arXiv2026

Expectation-Maximization algorithm to estimate the forcing parameter of a nonlinear McKean-Vlasov diffusion

In this article, we address the problem of estimating a forcing parameter in a stochastic differential equation inspired by a model that describes instantaneous turbulent kinetic energy. The stochastic differential equation we analyze is of the nonlinear McKean-Vlasov type, where the drift term depends on a power of the expected value of the solution, which also introduces nonlinearity in an algebraic sense. We propose an estimation algorithm based on the Expectation-Maximization framework and show the consistency of our method. We illustrate our findings through numerical experiments.

math.ST↗

arXiv2026

Simple repair policies and decompositions for semi-coherent systems with simultaneous failures

We consider semi-coherent binary systems that are subject to simultaneous failures of its components. These are systems whose components can be either working or failed; the system can also be working or failed depending on the state of the components; and repairing a component cannot cause the system to fail. We consider that one or more components can fail simultaneously, allowing us to model external shocks and disasters. For this, we use the L\'evy-frailty Marshall-Olkin (LFMO) multivariate distribution to model the failure times of the components. We aim to answer in which states of the system we should repair the components. This is a challenging question, as the number of repair policies grows super-exponentially in the number of components. To tackle this, we propose a simple family of repair policies, which we call $r$-out-of-$n$:R repair policies, where one repairs all failed components when the system fails or when there are $r$ or more failed components. Our main contribution is that we derive exact and simple expressions for key performance-evaluation quantities of the system operating under our proposed repair policies. That is, we give explicit expressions for the mean time-to-failure of the system, mean time-to-repair, probability of system-failure before repair, and component- and system-repair rate. We also give expressions for the expected cost and long-term average cost, when there are components' and system repair cost. The only relevant parameters involved in the derived expressions are the structural signature of the system, and the Laplace exponent associated to the LFMO distribution.

math.PR↗

arXiv2018

Synchronization of stochastic mean field networks of Hodgkin-Huxley neurons with noisy channels

In this work we are interested in a mathematical model of the collective behavior of a fully connected network of finitely many neurons, when their number and when time go to infinity. We assume that every neuron follows a stochastic version of the Hodgkin-Huxley model, and that pairs of neurons interact through both electrical and chemical synapses, the global connectivity being of mean field type. When the leak conductance is strictly positive, we prove that if the initial voltages are uniformly bounded and the electrical interaction between neurons is strong enough, then, uniformly in the number of neurons, the whole system synchronizes exponentially fast as time goes to infinity, up to some error controlled by (and vanishing with) the channels noise level. Moreover, we prove that if the random initial condition is exchangeable, on every bounded time interval the propagation of chaos property for this system holds (regardless of the interaction intensities). Combining these results, we deduce that the nonlinear McKean-Vlasov equation describing an infinite network of such neurons concentrates, as time goes to infinity, around the dynamics of a single Hodgkin-Huxley neuron with chemical neurotransmitter channels. Our results are illustrated and complemented with numerical simulations.

math.PR↗