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