On asymptotic inference in stochastic differential equations with time-varying covariates

Authors

Trisha Maitra, Indian Statistical Institute, Kolkata
Sourabh Bhattacharya, Indian Statistical Institute, Kolkata

Article Type

Research Article

Publication Title

Canadian Journal of Statistics

Abstract

In this article, we introduce a system of stochastic differential equations (SDEs) consisting of time-dependent covariates and consider both fixed and random effects. We also allow the functional part associated with the drift function to depend upon unknown parameters. For this general SDE system we establish consistency and asymptotic normality of the maximum likelihood estimator. We consider a Bayesian approach for learning about the population parameters, and prove consistency and asymptotic normality of the corresponding posterior distribution. We supplement our theoretical investigation with simulated and real data analyses, obtaining encouraging results in both cases. The Canadian Journal of Statistics 46: 635–655; 2018 © 2018 Statistical Society of Canada.

First Page

635

Last Page

655

DOI

10.1002/cjs.11471

Publication Date

12-1-2018

Comments

All Open Access, Green

Recommended Citation

Maitra, Trisha and Bhattacharya, Sourabh, "On asymptotic inference in stochastic differential equations with time-varying covariates" (2018). Journal Articles. 1116.
https://digitalcommons.isical.ac.in/journal-articles/1116