Stochastic elastic equation driven by fractional Brownian motion

Abstract

In this paper, we consider the stochastic elastic equation driven by a cylindrical fractional Brownian motion. The regularities of the solution to the linear stochastic problem corresponding to the stochastic elastic equation are proved. Then, we obtain the existence of the solution using the Picard iteration.

Keywords:

• Fractional Brownian motion
• Hurst parameter
• stochastic partial differential equations

AMS Subject Classifications:

• 60H15
• 65M06

Acknowledgements

The authors appreciate the handling editor and anonymous reviewers for their valuable comments to improve this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the Innovation Foundation of BUAA for PhD Graduates, the Beijing Natural Science Foundation (4152029) and the National Natural Science Foundation of China under grant 61271010.