We compare the large deviations between jump Markov processes and their diffusion approximations for the problem of escape from a domain. It is known that the escape times are generally asymptotically different, leading to a quantitative error. In this paper we show that the escape point can...

We consider a general class of piecewise-deterministic Markov processes with multiple time-scales. In line with recent results on the stochastic averaging principle for these processes, we obtain a description of their law through an asymptotic expansion. We further study the fluctuations around...

In this paper, we consider families of time Markov fields (or reciprocal classes) which have the same bridges as a Brownian diffusion. We characterize each class as the set of solutions of an integration by parts formula on the space of continuous paths . Our techniques provide a...

We prove a duality theorem for the stochastic optimal control problem with a convex cost function and show that the minimizer satisfies a class of forward-backward stochastic differential equations. As an application, we give an approach, from the duality theorem, to h-path processes for...

We consider a bidimensional Ornstein-Uhlenbeck process to describe the tissue microvascularization in anti-cancer therapy. Data are discrete, partial and noisy observations of this stochastic differential equation (SDE). Our aim is to estimate the SDE parameters. We use the main advantage of a...

Growth curve data consist of repeated measurements of a continuous growth process over time in a population of individuals. These data are classically analyzed by nonlinear mixed models. However, the standard growth functions used in this context prescribe monotone increasing growth and can fail...

This paper is a survey of existing estimation methods for pharmacokinetic/pharmacodynamic (PK/PD) models based on stochastic differential equations (SDEs). Most parametric estimation methods proposed for SDEs require high frequency data and are often poorly suited for PK/PD data which are...