Related papers: Statistical inference for discretely sampled stoch…
We study the problem of parameter estimation for discretely observed stochastic differential equations driven by small fractional noise. Under some conditions, we obtain strong consistency and rate of convergence of the least square…
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…
In this paper, we consider the problem of joint parameter estimation for drift and diffusion coefficients of a stochastic McKean-Vlasov equation and for the associated system of interacting particles. The analysis is provided in a general…
We consider a multidimensional diffusion X with drift coefficient b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)). The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a fixed interval [0,T].…
We study the estimation of time-homogeneous drift functions in multivariate stochastic differential equations with known diffusion coefficient, from multiple trajectories observed at high frequency over a fixed time horizon. We formulate…
We propose a contrast-based estimation method for Gaussian processes with time-inhomogeneous drifts, observed under high-frequency sampling. The process is modeled as the sum of a deterministic drift function and a stationary Gaussian…
We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small L\'{e}vy noises. We do not impose any moment condition on the driving L\'{e}vy process. Under certain regularity conditions…
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class…
Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by…
We study a least squares estimator for an unknown parameter in the drift coefficient of a path- distribution dependent stochastic differential equation involving a small dispersion parameter epsilon greater than zero. The estimator, based…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…
Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…
We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and…
We consider non-parametric Bayesian estimation of the drift coefficient of a one-dimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions that are…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
This paper deals with a copies-based continuously differentiable and strictly decreasing estimator of the drift function for stochastic differential equations defining recurrent diffusion processes. The first part of our paper deals with…
We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…