An Ornstein-Uhlenbeck diffusion process is considered as a model for the membrane potential activity of a single neuron. We assume that the neuron is subject to a sequence of inhibitory and excitatory post-synaptic potentials that occur with time-dependent rates. The resulting process is characterized by time-dependent drift. For this model, we construct the return process describing the membra...

The paper presents a cointegration model in continuous time, where the linear combinations of the integrated processes are modeled by a multivariate Ornstein-Uhlenbeck process. The integrated processes are defined as vector-valued Lévy processes with an additional noise term. Hence, if we observe the process at discrete time points, we obtain a multiple regression model. As an estimator for the...

In this article, we propose several quantization based stratified sampling methods to reduce the variance of a Monte-Carlo simulation. Theoretical aspects of stratification lead to a strong link between the problem of optimal Lquantization of a random variable and the variance reduction that can be achieved. We first emphasize on the consistency of quantization for designing strata in stratifie...

We review and extend recent developments on the statistical properties of Active Ornstein Uhlenbeck particles (AOUPs). In this simplest models, Gaussian white noise overdamped Brownian colloids is replaced by a colored noise. This suffice to grant system hallmark active matter, while still allowing for analytical progress. first detail perturbative derivation steady state AOUPs in small persist...