Ergodicity of stochastic smoking model and parameter estimation

Advances in Difference Equations

Mei Dong¹  Zhenzhong Zhang¹  Jinying Tong¹  Xuekang Zhang¹ 

[1] Department of Applied Mathematics, Donghua University, Shanghai, China

关键词: stochastic smoking model;    stationary distribution;    least squares estimation;    ergodic theory;    quadratic variation;   

DOI  :  10.1186/s13662-016-0997-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we first propose a stochastic smoking model driven by Brownian motion based on a deterministic smoking model. We show that when the coefficients of the noise are small, the smoking model is ergodic. We then estimate the drift coefficients of stochastic smoking model by a least squares estimation and the ergodic theory on the stationary distribution. Finally, we develop a new approach to estimating the diffusion coefficients. Computer simulations will be used to illustrate our theory.

【 授权许可】

CC BY