Nicolas Marie

Sensitivities via rough paths

Motivated by a problematic coming from mathematical finance, this paper is devoted to existing and additional results of continuity and differentiability of the Ito map associated to rough differential equations. These regularity results together with Malliavin calculus are applied to sensitivities analysis for stochastic differential equations driven by multidimensional Gaussian processes with continuous paths, especially fractional Brownian motions. Precisely, in that framework, results on computation of greeks for Itos stochastic differential equations are extended. An application in mathematical finance, and simulations, are provided.

A Distribution Free Interval Estimate for Coefficient Alpha

Scales are important tools for obtaining quantitative measures of theoretical constructs. Once a set of measures to be used in a scale is selected, reliability is commonly examined in order to assess their measurement quality. To date, Cronbach’s coefficient alpha is the most commonly reported index of measurement quality for assessing scale reliability. In this paper, an asymptotic distribution of the natural estimator of coefficient alpha is derived. A new interval estimate and a statistical test on the significance of the sample estimate of the coefficient are also presented. The proposed approach is compared to four popular methods commonly used to compute confidence intervals (CI) for alpha using a Monte Carlo simulation study. An R function for implementing the proposed CI approach is also provided.

On a fractional stochastic Hodgkin–Huxley model

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 multiplicative noise driven by a fractional Brownian motion, with a vector field satisfying the viability condition of Coutin and Marie for

Invariance for rough differential equations

\mathbb R\times [0,1]^3

Ergodicity of a generalized Jacobi equation and applications

. An application to the modeling of the membrane potential of nerve fibers damaged by a neuropathy is provided.

Buprenorphine is protective against the depressive effects of norbuprenorphine on ventilation.

In 1990, in Itos stochastic calculus framework, Aubin and Da Prato established a necessary and sufficient condition of invariance of a nonempty compact or convex subset C of R^d for stochastic differential equations (SDE) driven by a Brownian motion. In Lyons rough paths framework, this paper deals with an extension of Aubin and Da Pratos results to rough differential equations. A comparison theorem is provided, and the special case of differential equations driven by a fractional Brownian motion is detailed.

Tracking the opioid receptors on the way of desensitization.

Consider a 1-dimensional centered Gaussian process W with α-Holder continuous paths on the compact intervals of R+(α∈]0,1[) and W0=0, and X the local solution in rough paths sense of Jacobi’s equation driven by the signal W.