Parametric inference for multidimensional hypoelliptic diffusion with full observations

02/08/2018
by   Anna Melnykova, et al.
0

Multidimensional hypoelliptic diffusions arise naturally as models of neuronal activity. Estimation in those models is complex because of the degenerate structure of the diffusion coefficient. We build a consistent estimator of the drift and variance parameters with the help of a discretized log-likelihood of the continuous process in the case of fully observed data. We discuss the difficulties generated by the hypoellipticity and provide a proof of the consistency of the estimator. We test our approach numerically on the hypoelliptic FitzHugh-Nagumo model, which describes the firing mechanism of a neuron.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/18/2023

An approximate maximum likelihood estimator of drift parameters in a multidimensional diffusion model

For a fixed T and k ≥ 2, a k-dimensional vector stochastic differential ...
research
02/24/2020

Adaptive and non-adaptive estimation for degenerate diffusion processes

We discuss parametric estimation of a degenerate diffusion system from t...
research
05/28/2021

Parameter estimation in CKLS model by continuous observations

We consider a stochastic differential equation of the form dr_t = (a - b...
research
04/29/2020

Adaptive tests for parameter changes in ergodic diffusion processes from discrete observations

We consider the adaptive test for the parameter change in discretely obs...
research
07/24/2018

Contrast function estimation for the drift parameter of ergodic jump diffusion process

In this paper we consider an ergodic diffusion process with jumps whose ...
research
10/20/2022

The Network Structure of Unequal Diffusion

Social networks affect the diffusion of information, and thus have the p...
research
03/15/2019

Parametric estimation for a signal-plus-noise model from discrete time observations

This paper deals with the parametric inference for integrated signals em...

Please sign up or login with your details

Forgot password? Click here to reset