A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H > 1/2 is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.
@article{urn:eudml:doc:42846,
title = {Differential equations driven by fractional Brownian motion.},
journal = {Collectanea Mathematica},
volume = {53},
year = {2002},
pages = {55-81},
zbl = {1018.60057},
mrnumber = {MR1893308},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42846}
}
Nualart, David; Rascanu, Aurel. Differential equations driven by fractional Brownian motion.. Collectanea Mathematica, Tome 53 (2002) pp. 55-81. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42846/