Viability for Stochastic Differential Equations Driven by G-Brownian Motion
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In this paper, we prove a type of Nagumo theorem on viability properties for stochastic differential equations driven by G-Brownian motion (G-SDEs). In particular, an equivalent criterion is formulated through stochastic contingent and tangent sets. Moreover, by the approach of direct and inverse images for stochastic tangent sets we present checkable conditions which keep the solution of a given G-SDE evolving in some particular sets.
KeywordsStochastic viability Stochastic differential equation Stochastic tangent set G-Brownian motion
Mathematics Subject Classification (2010)60H30 60H10
The authors would like to thank the editor and the anonymous referee for their helpful discussions and suggestions.
- 27.Peng, S.: Nonlinear expectations and stochastic calculus under uncertainty (2010). arXiv:1002.4546v1