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.
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The authors would like to thank the editor and the anonymous referee for their helpful discussions and suggestions.
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Peng Luo: Research partially supported by National Science Foundation of China, “Research Fund for International Young Scientists” (No. 11550110184) and National Natural Science Foundation of China (No. 11671257).
Falei Wang: Research partially supported by the National Natural Science Foundation of China (No. 11601282), the Natural Science Foundation of Shandong Province (No. ZR2016AQ10) and the China Scholarship Council (No. 201606225002). Luo and Wang’s research was partially supported by the Tian Yuan Projection of the National Natural Sciences Foundation of China (Nos. 11526205 and 11626247) and the 111 Project (No. B12023).
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Luo, P., Wang, F. Viability for Stochastic Differential Equations Driven by G-Brownian Motion. J Theor Probab 32, 395–416 (2019). https://doi.org/10.1007/s10959-017-0791-z
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DOI: https://doi.org/10.1007/s10959-017-0791-z