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Journal of Theoretical Probability

, Volume 32, Issue 1, pp 395–416 | Cite as

Viability for Stochastic Differential Equations Driven by G-Brownian Motion

  • Peng Luo
  • Falei WangEmail author
Article
  • 219 Downloads

Abstract

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.

Keywords

Stochastic viability Stochastic differential equation Stochastic tangent set G-Brownian motion 

Mathematics Subject Classification (2010)

60H30 60H10 

Notes

Acknowledgements

The authors would like to thank the editor and the anonymous referee for their helpful discussions and suggestions.

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Zhongtai Securities Institute for Financial StudiesShandong UniversityJinanChina
  2. 2.Department of MathematicsETH ZurichZurichSwitzerland
  3. 3.Zhongtai Securities Institute for Financial Studies and Institute for Advanced ResearchShandong UniversityJinanChina

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