Related papers: Update estimation of diffusion parameter observed …

In this paper we consider the problem of estimating a parameter of a probability distribution when we have some prior information on a nuisance parameter. We start by the very simple case where we know perfectly the value of the nuisance…

In this paper we consider the filtering of partially observed multi-dimensional diffusion processes that are observed regularly at discrete times. We assume that, for numerical reasons, one has to time-discretize the diffusion process which…

This paper proposes feasible asymptotically efficient estimators for a certain class of Gaussian noises with self-similar and stationary properties, which includes the fractional Gaussian noise, under high frequency observations. In this…

This paper studies an approximation method for the log-likelihood function of a nonlinear diffusion process using the bridge of the diffusion. The main result (Theorem \refthm:approx) shows that this approximation converges uniformly to the…

We study the problem of parameter estimation using maximum likelihood for fast/slow systems of stochastic differential equations. Our aim is to shed light on the problem of model/data mismatch at small scales. We consider two classes of…

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces \emph{separably estimable} observation models that generalize the…

In this paper the filtering of partially observed diffusions, with discrete-time observations, is considered. It is assumed that only biased approximations of the diffusion can be obtained, for choice of an accuracy parameter indexed by…

To ensure high quality outputs, it is important to quantify the epistemic uncertainty of diffusion models. Existing methods are often unreliable because they mix epistemic and aleatoric uncertainty. We introduce a method based on Fisher…

This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function, which can equip distributed networks with robust learning capability in the presence of impulsive interference. In order to…

This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters…

We consider statistical inference for a class of continuous semimartingale regression models based on high-frequency observations subject to contamination by finite-activity jumps and spike noise. By employing density-power weighting and…

We consider efficient estimation of the Euclidean parameters in a generalized partially linear additive models for longitudinal/clustered data when multiple covariates need to be modeled nonparametrically, and propose an estimation…

We study the problem of parametric estimation for continuously observed stochastic differential equation driven by fractional Brownian motion. Under some assumptions on drift and diffusion coefficients, we construct maximum likelihood…

We study the asymptotic theory of misspecified models for diffusion processes with noisy nonsynchronous observations. Unlike with correctly specified models, the original maximum-likelihood-type estimator has an asymptotic bias under the…

This paper introduces a Monte Carlo method for maximum likelihood inference in the context of discretely observed diffusion processes. The method gives unbiased and a.s.\@ continuous estimators of the likelihood function for a family of…

For a fixed $T$ and $k \geq 2$, a $k$-dimensional vector stochastic differential equation $dX_t=\mu(X_t, \theta)dt+\nu(X_t)dW_t,$ is studied over a time interval $[0,T]$. Vector of drift parameters $\theta$ is unknown. The dependence in…

This work aims at making a comprehensive contribution in the general area of parametric inference for discretely observed diffusion processes. Established approaches for likelihood-based estimation invoke a time-discretisation scheme for…

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

We consider a process $X^\ve$ solution of a stochastic Volterra equation with an unknown parameter $\theta^\star$ in the drift function. The Volterra kernel is singular near zero, exhibiting a behavior comparable to $K\_0(u)=cu^{\alpha-1}…

The most common way of estimating the anomalous diffusion exponent from single-particle trajectories consists in a linear fitting of the dependence of the time averaged mean square displacement on the lag time at the log-log scale. However,…