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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.)