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Deterministic characterization of viability for stochasticdifferential equation driven by fractional Brownian motion∗∗∗

Published online by Cambridge University Press:  22 November 2011

Tianyang Nie  and
Aurel Răşcanu
Tianyang Nie
Affiliation:
School of Mathematics, Shandong University, Jinan, Shandong 250100, P.R. China. [email protected] ; [email protected] Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Blvd, No. 11, 700506 Iasi, Romania; [email protected]
Aurel Răşcanu
Affiliation:
Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Blvd, No. 11, 700506 Iasi, Romania; [email protected] “Octav Mayer” Mathematics Institute of the Romanian Academy, Carol I Blvd, No. 8, 700506 Iasi, Romania
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Abstract

In this paper, using direct and inverse images for fractional stochastic tangent sets, weestablish the deterministic necessary and sufficient conditions which control that thesolution of a given stochastic differential equation driven by the fractional Brownianmotion evolves in some particular sets K. As a consequence, a comparisontheorem is obtained.

Keywords

Stochastic viabilitystochastic differential equationstochastic tangent setfractional Brownian motion
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 915 - 929
Copyright
© EDP Sciences, SMAI, 2011

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