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Invariance for rough differential equations

Author

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  • Coutin, Laure
  • Marie, Nicolas

Abstract

In 1990, in Itô’s stochastic calculus framework, Aubin and Da Prato established a necessary and sufficient condition of invariance of a nonempty compact or convex subset C of Rd (d∈N∗) for stochastic differential equations (SDE) driven by a Brownian motion. In Lyons rough paths framework, this paper deals with an extension of Aubin and Da Prato’s results to rough differential equations. A comparison theorem is provided, and the special case of differential equations driven by a fractional Brownian motion is detailed.

Suggested Citation

  • Coutin, Laure & Marie, Nicolas, 2017. "Invariance for rough differential equations," Stochastic Processes and their Applications, Elsevier, vol. 127(7), pages 2373-2395.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:7:p:2373-2395
    DOI: 10.1016/j.spa.2016.11.002
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    References listed on IDEAS

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    1. Alexander Melnikov & Yuliya Mishura & Georgiy Shevchenko, 2015. "Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations," Methodology and Computing in Applied Probability, Springer, vol. 17(1), pages 169-188, March.
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