Open Access
2023 On the capacity for degenerated G-Brownian motion and its application
Xiaojuan Li, Xinpeng Li
Author Affiliations +
Electron. Commun. Probab. 28: 1-9 (2023). DOI: 10.1214/23-ECP565

Abstract

In this paper, the capacity c({BTA}) of degenerated G-Brownian motion BT 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 c({BT=a})>0 for each aR in the degenerated case we study here. As an application, we show that IA(BT) has no quasi-continuous version unless A= or R.

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

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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

Information

Received: 25 November 2022; Accepted: 12 November 2023; Published: 2023
First available in Project Euclid: 22 November 2023

Digital Object Identifier: 10.1214/23-ECP565

Subjects:
Primary: 35D40 , 60A10

Keywords: G-Brownian motion , G-capacity , g-expectation , quasi-continuity , viscosity solution

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