Existence of solution for stochastic differential equations driven by \(G\)-Lévy process with discontinuous coefficients

DOI10.1186/S13662-017-1242-YzbMath1444.60058OpenAlexW2734280272WikidataQ59525038 ScholiaQ59525038MaRDI QIDQ1726216

Mingxia Yuan, Bingjun Wang

Publication date: 19 February 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-017-1242-y

zbMATH Keywords

discontinuous coefficientsstochastic differential equations\(G\)-Lévy processupper and lower solution

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear processes (e.g., (G)-Brownian motion, (G)-Lévy processes) (60G65)

Related Items (4)

Path independence of the additive functionals for stochastic differential equations driven by \(G\)-Lévy processes ⋮ The Carathéodory approximation scheme for stochastic differential equations with G‐Lévy process ⋮ Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control ⋮ Exponential stability of solutions to stochastic differential equations driven by \(G\)-Lévy process

Cites Work

• On representation theorem of sublinear expectation related to \(G\)-Lévy process and paths of \(G\)-Lévy process
• Martingale representation theorem for the \(G\)-expectation
• Stopping times and related Itô's calculus with \(G\)-Brownian motion
• Function spaces and capacity related to a sublinear expectation: application to \(G\)-Brownian motion paths
• Filtration consistent nonlinear expectations and evaluations of contingent claims
• \(G\)-Lévy processes under sublinear expectations
• Multi-dimensional \(G\)-Brownian motion and related stochastic calculus under \(G\)-expectation
• On fixed points of multifunctions in ordered spaces

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