Well-posedness for SDEs driven by different type of noises

TL;DR

This paper establishes the existence and uniqueness of strong solutions for stochastic differential equations driven by mixed noises, including partial alpha-stable and Brownian noise, with singular coefficients, using regularity of Kolmogorov equations.

Contribution

It introduces a novel approach to prove well-posedness for SDEs driven by mixed noises with singular coefficients, expanding the theoretical understanding in this area.

Findings

Proves strong solution existence for SDEs with partial alpha-stable and Brownian noise.

Establishes uniqueness of solutions under singular coefficient conditions.

Utilizes regularity of degenerate mixed Kolmogorov equations for the proof.

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.