24 citations · 63 across the 20 of their papers we have counts for
21 papers
Closed-form modeling of neuronal spike train statistics using multivariate Hawkes cumulants
Nicolas Privault, Michèle Thieullen
We derive exact analytical expressions for the cumulants of any orders of neuronal membrane potentials driven by spike trains in a multivariate Hawkes process model with excitation…
Optimal control of infinite-dimensional Piecewise Deterministic Markov Processes: a BSDE approach. Application to the control of an excitable cell membrane
Elena Bandini, Michele Thieullen
In this paper we consider the optimal control of Hilbert space-valued infinite-dimensional Piecewise Deterministic Markov Processes (PDMP) and we prove that the corresponding value…
Thinning and Multilevel Monte Carlo for Piecewise Deterministic (Markov) Processes. Application to a stochastic Morris-Lecar model
Vincent Lemaire, Michèle Thieullen, Nicolas Thomas
In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also es…
Stochastic representation of tau functions of Korteweg-de Vries equation
Michèle Thieullen, Alexis Vigot
In this paper we express tau functions for the Korteweg de Vries (KdV) equation, as Laplace transforms of iterated Skorohod integrals. Our main tool is the notion of Fredholm deter…
Iterated stochastic processes : simulation and relationship with high order partial differential equations
Michèle Thieullen, Alexis Vigot
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated proc…
Minimal time spiking in various ChR2-controlled neuron models
Vincent Renault, Michèle Thieullen, Emmanuel Trélat
We use conductance based neuron models and the mathematical modeling of Optogenetics to define controlled neuron models and we address the minimal time control of these affine syst…