Nonparametric estimation of trend for SDEs with delay driven by a fractional brownian motion with small noise

Abstract

We investigate the problem of nonparametric estimation of the trend for stochastic differential equations with delay and driven by a fractional Brownian motion through the method of kernel-type estimation for the estimation of a probability density function.

Keywords:

• Nonparametric estimation
• estimation of trend
• stochastic differential equation with delay
• kernel method of estimation
• fractional Brownian motion

AMS Subject Classification:

• 62M09
• 60G22

Acknowledgments

The author thanks the referee for his/her suggestions for dealing with the problem in the general case. This work was supported under the scheme “INSA Senior Scientist” of the Indian National Science Academy at the CR Rao Advanced Institute of Mathematics, Statistics and Computer Science, Hyderabad, India.