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Properties of Solutions to Stochastic Set Differential Equations under Non‐Lipschitzian Coefficients

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  • Weiyin Fei
  • Yunhe Li
  • Chen Fei

Abstract

A class of stochastic set differential equations (SSDEs) with non‐Lipschitzian coefficients is investigated. We first give the preliminaries on the stochastic set differential equations. Then the nonexplosion of solutions to the SSDEs is discussed. Moreover, the existence and uniqueness of the solutions to SSDEs are proven. Finally, the continuous dependence of the solutions to SSDEs is studied.

Suggested Citation

  • Weiyin Fei & Yunhe Li & Chen Fei, 2014. "Properties of Solutions to Stochastic Set Differential Equations under Non‐Lipschitzian Coefficients," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:381972
    DOI: 10.1155/2014/381972
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    References listed on IDEAS

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    2. Michał Kisielewicz, 2013. "Stochastic Differential Inclusions and Applications," Springer Optimization and Its Applications, Springer, edition 127, number 978-1-4614-6756-4, April.
    3. Mariusz Michta, 1997. "Continuity properties of solutions of multivalued equations with white noise perturbation," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-10, January.
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