We here investigate the well-posedness of a networked integrate-andfire model describing an infinite population of neurons which interact with one another through their common statistical… (More)

We introduce Monte Carlo methods to compute the solution of elliptic equations with pure Neumann boundary conditions. We first prove that the solution obtained by the stochastic representation has a… (More)

In this paper, we solve explicitly the optimal stopping problem with random discounting and an additive functional as cost of observations for a regular linear diffusion. We also extend the results… (More)

The aim of the present paper is to construct a stochastic process, whose law is the solution of the Smoluchowski’s coagulation equation. We introduce first a modified equation, dealing with the… (More)

We aim to compare financial technical analysis techniques to strategies which depend on a mathematical model. In this paper, we consider the moving average indicator and an investor using a risky… (More)

Motivated by some applications in neurosciences, we here collect several estimates for the density of the first hitting time of a threshold by a nonhomogeneous one-dimensional diffusion process and… (More)

In this study, we compare the performance of trading strategies based on possibly mis-specified mathematical models with a trading strategy based on a technical trading rule. In both cases, the… (More)

We generalize the exact simulation algorithm of one dimensional solution of SDE proposed by Beskos et al. [6]. We apply Malliavin Calculus to simulate exactly the greeks, that is the derivatives with… (More)

We consider a new model of individual neuron of Integrate-and-Fire (IF) type with fractional noise. The correlations of its spike trains are studied and proved to have long memory, unlike classical… (More)