Abstract
In this paper, the capacity of degenerated G-Brownian motion for arbitrary Borel set A is calculated via the viscosity solution of G-heat equation. In particular, unlike the classical Brownian motion and non-degenerated G-Brownian motion which do not weight points, we obtain for each in the degenerated case we study here. As an application, we show that has no quasi-continuous version unless or .
Funding Statement
Supported by NSF of Shandong Province (No. ZR2021MA018), National Key R&D Program of China (No. 2018YFA0703900) and NSF of China (No. 11671231 and 11601281).
Citation
Xiaojuan Li. Xinpeng Li. "On the capacity for degenerated G-Brownian motion and its application." Electron. Commun. Probab. 28 1 - 9, 2023. https://doi.org/10.1214/23-ECP565
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