Related papers: Drift parameter estimation for nonlinear reflected…
We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on the…
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion…
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 study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current…
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 the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…
In this article, we present the least squares estimator for the drift parameter in a linear regression model driven by the increment of a fractional Brownian motion sampled at random times. For two different random times, Jittered and…
We discuss the problem of parameter estimation in nonlinear stochastic differential equations based on sampled time series. A central message from the theory of integrating stochastic differential equations is that there exists in general…
We take into consideration generalization bounds for the problem of the estimation of the drift component for ergodic stochastic differential equations, when the estimator is a ReLU neural network and the estimation is non-parametric with…
The likelihood functions for discretely observed nonlinear continuous-time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
Consider discrete time observations (X_{\ell\delta})_{1\leq \ell \leq n+1}$ of the process $X$ satisfying $dX_t= \sqrt{V_t} dB_t$, with $V_t$ a one-dimensional positive diffusion process independent of the Brownian motion $B$. For both the…
This paper presents a numerical method to implement the parameter estimation method using response statistics that was recently formulated by the authors. The proposed approach formulates the parameter estimation problem of It\^o drift…
In this paper, we investigate the parameter estimation problem for reflected OU processes. Both the estimates based on continuously observed processes and discretely observed processes are considered. The explicit formulas for the…
We consider a one-dimensional diffusion process $(X_t)$ which is observed at $n+1$ discrete times with regular sampling interval $\Delta$. Assuming that $(X_t)$ is strictly stationary, we propose nonparametric estimators of the drift and…
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…
We study the Nadaraya-Watson (N-W) estimator for the drift function of two-sided reflected stochastic processes. We propose a discrete-type N-W estimator and a continuous-type N-W estimator based on the discretely observed processes and…
In this paper, we consider the robust adaptive non parametric estimation problem for the drift coefficient in diffusion processes. An adaptive model selection procedure, based on the improved weighted least square estimates, is proposed.…
We consider the problem of asymptotically efficient estimation of drift parameters of the ergodic fractional Ornstein-Uhlenbeck process under continuous observations when the Hurst parameter $H<1/2$ and the mean of its stationary…
We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new…