Harnack inequalities for functional SDEs driven by subordinate Volterra-Gaussian processes

Abstract

Based on the Girsanov theorem for a kind of Volterra-Gaussian process, which are the generalization of fractional Brownian motion, Liouville fractional Brownian motion, and fractional Ornstein-Uhlenbeck process, we establish the Harnack inequalities for a class of stochastic functional differential equations driven by a kind of Volterra-Gaussian processes with a subordinator by an approximation technique. Some known results have been generalized and improved.

Keywords:

• Harnack inequality
• Volterra-Gaussian processes
• Subordinator
• Sonine pairs

2000 Mathematics Subject Classification(s)::

• 60H15
• 60G15
• 60H05

Disclosure statement

No potential conflict of interest was reported by the author(s).