Similarity Between Two Stochastic Differential Systems
Abstract
The main focus of this paper is to explore how much similarity between two stochastic differential systems. Motivated by the conjugate theory of stochastic dynamic systems, we study the relationship between two systems by finding homeomorphic mappings . Particularly, we use the minimizer to measure the degree of similarity. Under appropriate assumptions, we give sufficient and necessary conditions for the existence of the minimizer . The former result can be regarded as a strong law of large numbers, while the latter is a stochastic maximum principle. Finally, we provide different examples of stochastic systems and an application to stochastic Hartman Grobman theorem. Thus, the results illustrate what is the similarity, extending the conjugacy in stochastic dynamical systems.
Cite
@article{arxiv.2310.10901,
title = {Similarity Between Two Stochastic Differential Systems},
author = {Xiaoying Wang and Yuecai Han and Yong Li},
journal= {arXiv preprint arXiv:2310.10901},
year = {2023}
}