Volume 18, Number 4, October-December 2012
|Page(s)||915 - 929|
|Published online||22 November 2011|
Deterministic characterization of viability for stochastic differential equation driven by fractional Brownian motion∗,∗∗
1 School of Mathematics, Shandong
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2 Faculty of Mathematics, “Alexandru Ioan Cuza” University, Carol I Blvd, No. 11, 700506 Iasi, Romania
3 “Octav Mayer” Mathematics Institute of the Romanian Academy, Carol I Blvd, No. 8, 700506 Iasi, Romania
Revised: 17 July 2011
In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets K. As a consequence, a comparison theorem is obtained.
Mathematics Subject Classification: 60H10 / 60H20 / 60G22
Key words: Stochastic viability / stochastic differential equation / stochastic tangent set / fractional Brownian motion
© EDP Sciences, SMAI, 2011
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