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

Hu, Yaozhong; Nualart, David

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].

Reviewer: Melvin D. Lax (Long Beach)

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