Parameter Estimation for the Continuous Time Stochastic Logistic Diffusion Model

Abstract

In this paper, the parameter estimation problem is investigated for the continuous time stochastic logistic diffusion system. A new continuous process is built based on the likelihood ratio scheme, the Radon-Nikodym derivative and the explicit expressions of the error of estimation are given under this new continuous process. By using the random time transformations, law of large numbers for martingales, law of iterated logarithm and stationary distribution of solution, the consistency property are proved for the estimation error. Finally, a numerical simulation is presented to demonstrate the effectiveness of the proposed method in this paper.

Estimating Parameters of Large CTMP from Single Trajectory with Application to Stochastic Network Epidemics Models

“…Deterministic models are derived using mean-field approximation, which assume full-mixing (i.e every individual interacts with all other individuals with the same probability) and analyze the asymptotic (assuming an infinitely large population) behavior stochastic models. Classic epidemics models are time-series based; there are many approaches to learning the dynamics parameters of classic epidemics models [5], [6], [7], [8], [9].…”

“…Estimate q(H i , H i ) from the given observations using equation (6). Estimate the corresponding sample variance var( q(H i , H i )) to determine the diagonal entries of W .…”