23 citations · 172 across the 27 of their papers we have counts for
12 papers · 1 filter
On a Set-Valued Young Integral with Applications to Differential Inclusions
Laure Coutin, Nicolas Marie, Paul Raynaud de Fitte
We present a new Aumann-like integral for a Hölder multifunction with respect to a Hölder signal, based on the Young integral of a particular set of Hölder selections. This restric…
Almost Periodic and Periodic Solutions of Differential Equations Driven by the Fractional Brownian Motion with Statistical Application
Nicolas Marie, Paul Raynaud de Fitte
We show that the unique solution to a semilinear stochastic differential equation with almost periodic coefficients driven by a fractional Brownian motion is almost periodic in a s…
Nonparametric Estimation in Fractional SDE
Fabienne Comte, Nicolas Marie
This paper deals with the consistency and a rate of convergence for a Nadaraya-Watson estimator of the drift function of a stochastic differential equation driven by an additive fr…
Sweeping Processes Perturbed by Rough Signals
Charles Castaing, Nicolas Marie, Paul Raynaud De Fitte
This paper deals with the existence, the uniqueness and an approximation scheme of the solution to sweeping processes perturbed by a continuous signal of finite -variation with…
On a Fractional Stochastic Hodgkin-Huxley Model
Laure Coutin, Jean-Marc Guglielmi, Nicolas Marie
The model studied in this paper is a stochastic extension of the so-called neuron model introduced by Hodgkin and Huxley. In the sense of rough paths, the model is perturbed by a m…
On a Constrained Fractional Stochastic Volatility Model
Nicolas Marie
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differenti…