| Issue |
ESAIM: COCV
Volume 18, Number 4, October-December 2012
|
|
|---|---|---|
| Page(s) | 915 - 929 | |
| DOI | https://doi.org/10.1051/cocv/2011188 | |
| Published online | 22 November 2011 | |
Deterministic characterization of viability for stochastic differential equation driven by fractional Brownian motion∗,∗∗
1 School of Mathematics, Shandong
University, Jinan,
Shandong
250100, P.R.
China
nietianyang@163.com ; tianyang.nie@uaic.ro
2
Faculty of Mathematics, “Alexandru Ioan Cuza”
University, Carol I Blvd, No.
11, 700506
Iasi,
Romania
aurel.rascanu@uaic.ro
3
“Octav Mayer” Mathematics Institute of the Romanian Academy,
Carol I Blvd, No.
8, 700506
Iasi,
Romania
Received:
8
February
2011
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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