## Differential equations driven by Hölder continuous functions of order greater than $$1/2$$.(English)Zbl 1144.34038

Benth, Fred Espen (ed.) et al., Stochastic analysis and applications. The Abel symposium 2005. Proceedings of the second Abel symposium, Oslo, Norway, July 29 – August 4, 2005, held in honor of Kiyosi Itô. Berlin: Springer (ISBN 978-3-540-70846-9/hbk). Abel Symposia 2, 399-413 (2007).
Theorems are proved that provide upper bounds for the solutions of differential equations driven by Hölder continuous functions with order greater than $$1/2$$.
As a corollary to these results, the existence of moments of solutions of stochastic differential equations driven by fractional Brownian motion with Hurst parameter greater than $$1/2$$ is established.
For the entire collection see [Zbl 1113.60006].

### MSC:

 34F05 Ordinary differential equations and systems with randomness 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 34C11 Growth and boundedness of solutions to ordinary differential equations
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