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The aim of this paper is twofold. Firstly, we derive upper and lowernon-Gaussian bounds for the densities of the marginal laws of the solutions tobackward stochastic differential equations (BSDEs) driven by fractionalBrownian motions. Our arguments consist of utilising a relationship betweenfractional BSDEs and quasilinear partial differential equations of mixed type,together with the profound Nourdin-Viens formula. In the linear case, upper andlower Gaussian bounds for the densities and the tail probabilities of solutionsare obtained with simple arguments by their explicit expressions in terms ofthe quasi-conditional expectation. Secondly, we are concerned with Gaussianestimates for the densities of a BSDE driven by a Gaussian process in themanner that the solution can be established via an auxiliary BSDE driven by aBrownian motion. Using the transfer theorem we succeed in deriving Gaussianestimates for the solutions.

Density estimates for the solutions of backward stochastic differential equations driven by Gaussian processes