Geodesic
Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion
ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 915-929
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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.

DOI : 10.1051/cocv/2011188
Classification : 60H10, 60H20, 60G22
Keywords: stochastic viability, stochastic differential equation, stochastic tangent set, fractional brownian motion 
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     title = {Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {915--929},
     year = {2012},
     publisher = {EDP-Sciences},
     volume = {18},
     number = {4},
     doi = {10.1051/cocv/2011188},
     mrnumber = {3019464},
     zbl = {1263.60052},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2011188/}
}
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Nie, Tianyang; Răşcanu, Aurel. Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 915-929. doi: 10.1051/cocv/2011188

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