Abstract
This note is devoted to show how to push forward the algebraic integration setting in order to treat differential systems driven by a noisy input with Hölder regularity greater than \(1/4\). After recalling how to treat the case of ordinary stochastic differential equations, we mainly focus on the case of delay equations. A careful analysis is then performed in order to show that a fractional Brownian motion with Hurst parameter H > 1 ∕ 4 fulfills the assumptions of our abstract theorems.
AMS Classification. 60H05, 60H07, 60G15.
Dedicated to Ali Süleyman Üstünel on occasion of his 60th birthday
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Acknowledgements
S. Tindel is partially supported by the ANR grant ECRU. I. Torrecilla is partially supported by the grant MTM2009-07203 from the Dirección General de Investigación, Ministerio de Ciencia e Innovacin, Spain. I. Torrecilla wishes to thank the IECN (Institut Élie Cartan Nancy) for its warm hospitality during a visit in 2008, which served to settle the basis of the current chapter.
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Tindel, S., Torrecilla, I. (2012). Some Differential Systems Driven by a fBm with Hurst Parameter Greater than 1/4. In: Decreusefond, L., Najim, J. (eds) Stochastic Analysis and Related Topics. Springer Proceedings in Mathematics & Statistics, vol 22. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29982-7_8
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