Properties of \(G\)-martingales with finite variation and the application to \(G\)-Sobolev spaces

DOI10.1016/j.spa.2018.07.002zbMath1488.60112arXiv1607.00616OpenAlexW2962869534MaRDI QIDQ2000140

Yongsheng Song

Publication date: 28 June 2019

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.00616

zbMATH Keywords

unique decomposition\(G\)-martingales with finite variation\(G\)-Sobolev spacesgeneralized \(G\)-Itô processes

Mathematics Subject Classification ID

Generalizations of martingales (60G48) Martingales with continuous parameter (60G44)

Related Items (9)

Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential equations ⋮ Multi-dimensional BSDEs driven by G-Brownian motion and related system of fully nonlinear PDEs ⋮ Backward stochastic differential equations driven by \(G\)-Brownian motion with double reflections ⋮ Survey on path-dependent PDEs ⋮ BSDEs driven by \(G\)-Brownian motion with non-Lipschitz coefficients ⋮ Probabilistic approach to singular perturbations of viscosity solutions to nonlinear parabolic PDEs ⋮ An averaging principle for nonlinear parabolic PDEs via FBSDEs driven by \(G\)-Brownian motion ⋮ Quadratic \(G\)-BSDEs with convex generators and unbounded terminal conditions ⋮ Stability of solutions of Caputo fractional stochastic differential equations

Cites Work

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• Characterizations of processes with stationary and independent increments under \(G\)-expectation
• Backward stochastic differential equations driven by \(G\)-Brownian motion
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• A complete representation theorem for G-martingales

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