Integration by parts formula and applications for SDEs with Lévy noise. (Chinese. English summary) Zbl 1488.60154
Summary: By using the Malliavin calculus and finite jump approximations, the Driver-type integration by parts formula is established for the semigroup associated to stochastic differential equations with noises containing a subordinate Brownian motion. As applications, the shift Harnack inequality and heat kernel estimates are derived. The main results are illustrated by SDEs driven by \(\alpha\)-stable like processes.
MSC:
60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
26B20 | Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.) |