Harnack inequalities for SDEs driven by subordinate Brownian motions
The central aim of this work is to investigate Harnack inequalities for stochastic differential equations (SDEs) driven by subordinate Brownian motions. Some basic notations for subordinate Brownian motions are recalled. It is mentioned that subordinate Brownian motion is obtained by replacing the time of Brownian motion by an independent subordinator, and this fact allows to study subordinate Brownian motion by non-random time-changed Brownian motion. Further, inhomogeneous multidimensional SDEs with subordinate Brownian motion are studied under conditions that guarantee existence, uniqueness and non-explosion of the solutions. It is explained that when the underlying semigroup is not regular enough to satisfy the gradient estimate, the coupling method turned out to be very efficient to establish Harnack type inequalities. By using regularization approximations of the underlying subordinator and a gradient estimate approach, the authors get the dimension-independent Harnack inequalities for the inhomogeneous semigroup associated with a class of SDEs with Lévy noise containing a subordinate Brownian motion.
scientific article; zbMATH DE number 6380666
scientific article