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Lévy’s martingale characterization and reflection principle of \(G\)-Brownian motion. (English) Zbl 1479.60145

Summary: In this paper, by a new kind of discrete product space method for martingales, we obtain Lévy’s martingale characterization of \(G\)-Brownian motion without the nondegenerate condition. Based on this characterization, we prove the reflection principle of \(G\)-Brownian motion. Furthermore, we use Krylov’s estimate to get the reflection principle of the general \(\tilde{G}\)-Brownian motion.

MSC:

60H30 Applications of stochastic analysis (to PDEs, etc.)
60G65 Nonlinear processes (e.g., \(G\)-Brownian motion, \(G\)-Lévy processes)
60G44 Martingales with continuous parameter
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