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.
Keywords: stochastic viability, stochastic differential equation, stochastic tangent set, fractional brownian motion
@article{COCV_2012__18_4_915_0,
author = {Nie, Tianyang and R\u{a}\c{s}canu, Aurel},
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 = {https://www.numdam.org/articles/10.1051/cocv/2011188/}
}
TY - JOUR AU - Nie, Tianyang AU - Răşcanu, Aurel TI - Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 915 EP - 929 VL - 18 IS - 4 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2011188/ DO - 10.1051/cocv/2011188 LA - en ID - COCV_2012__18_4_915_0 ER -
%0 Journal Article %A Nie, Tianyang %A Răşcanu, Aurel %T Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 915-929 %V 18 %N 4 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2011188/ %R 10.1051/cocv/2011188 %G en %F COCV_2012__18_4_915_0
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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