Existence and transportation inequalities for fractional stochastic differential equations

Authors: ABDELGHANI OUAHAB, MUSTAPHA BELABBAS, JOHNNY HENDERSON, FETHI SOUNA

Abstract: 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.

Keywords: Fractional differential equations, fractional integral, fractional derivative, Mittag-Leffler functions, fixed point, stochastic equation, transportation inequality, Wasserstein distance, entropy

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