相关论文: Non-parametric estimation of Stochastic Differenti…
In the present paper, we consider that $N$ diffusion processes $X^1,\dots,X^N$ are observed on $[0,T]$, where $T$ is fixed and $N$ grows to infinity. Contrary to most of the recent works, we no longer assume that the processes are…
We investigate the problem of nonparametric estimation of the trend for stochastic differential equations with delay and driven by a fractional Brownian motion through the method of kernel-type estimation for the estimation of a probability…
In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
In this paper, high-order moment, even exponential moment, estimates are established for the H\"older norm of solutions to stochastic differential equations driven by fractional Brownian motion whose drifts are measurable and have linear…
We study asymptotic error distributions associated with standard approximation scheme for one-dimensional stochastic differential equations driven by fractional Brownian motions. This problem was studied by, for instance, Gradinaru-Nourdin…
The paper deals with projection estimators of the density of the stationary solution $X$ to a differential equation driven by the fractional Brownian motion under a dissipativity condition on the drift function. A model selection method is…
We consider a stochastic differential equation involving standard and fractional Brownian motion with unknown drift parameter to be estimated. We investigate the standard maximum likelihood estimate of the drift parameter, two non-standard…
We consider the inference problem for parameters in stochastic differential equation models from discrete time observations (e.g. experimental or simulation data). Specifically, we study the case where one does not have access to…
Stochastic differential equations and stochastic dynamics are good models to describe stochastic phenomena in real world. In this paper, we study N independent stochastic processes Xi(t) with real entries and the processes are determined by…
We study the maximum likelihood estimator of the drift parameters of a stochastic differential equation, with both drift and diffusion coefficients constant on the positive and negative axis, yet discontinuous at zero. This threshold…
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 discuss the distribution of various estimators for extracting the diffusion constant of single Brownian trajectories obtained by fitting the squared displacement of the trajectory. The analysis of the problem can be framed in terms of…
In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is…
Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the…
We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…
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…
The movement of a particle described by Brownian motion is quantified by a single parameter, $D$, the diffusion constant. The estimation of $D$ from a discrete sequence of noisy observations is a fundamental problem in biological single…
We consider the problem of estimating the roughness of the volatility process in a stochastic volatility model that arises as a nonlinear function of fractional Brownian motion with drift. To this end, we introduce a new estimator that…
We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…