G-capacity under degenerate case and its application

Abstract

In this paper, we first find a type of viscosity solution of $G$-heat equation under degenerate case, and then obtain the related $G$-capacity $c(\{B_T\in A\})$ for any Borel set $A$. Furthermore, we prove that $I_A(B_T)$ has no quasi-continuous version when it is not a constant function.

10 pages

References in corpus (2)

• Improving Value-at-Risk prediction under model uncertainty
• A monotone scheme for G-equations with application to the explicit convergence rate of robust central limit theorem