In this work, we establish the existence and uniqueness of solutions for a fractional stochastic differential equation driven by countably many Brownian motions on bounded and unbounded intervals. Also, we study the continuous dependence of solutions on initial data. Finally, we establish the transportation quadratic cost inequality for some classes of fractional stochastic equations and continuous dependence of solutions with respect Wasserstein distance.
OUAHAB, ABDELGHANI; BELABBAS, MUSTAPHA; HENDERSON, JOHNNY; and SOUNA, FETHI
"Existence and transportation inequalities for fractional stochastic differential equations,"
Turkish Journal of Mathematics: Vol. 46:
3, Article 3.
Available at: https://journals.tubitak.gov.tr/math/vol46/iss3/3