Well-posedness for SDEs driven by different type of noises

Abstract

We show the existence and uniqueness of strong solutions for stochastic differential equation driven by partial $\alpha$-stable noise and partial Brownian noise with singular coefficients. The proof is based on the regularity of degenerate mixed type Kolmogorov equation.

References in corpus (3)

• Noise Prevents Singularities in Linear Transport Equations
• Ergodicity of stochastic differential equations with jumps and singular coefficients
• Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient