Existence and stability of solutions to highly nonlinear stochastic differential delay equations driven by \(G\)-Brownian motion. (English) Zbl 1438.60071
Summary: Under linear expectation (or classical probability), the stability for stochastic differential delay equations (SDDEs), where their coefficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper, by using Peng’s \(G\)-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by \(G\)-Brownian motion (\(G\)-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to \(G\)-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear \(G\)-SDDEs.
MSC:
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 93E15 | Stochastic stability in control theory |
Keywords:
stochastic differential delay equation; sublinear expectation; existence and uniqueness; \(G\)-Brownian motion; stability and boundednessReferences:
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