  To study the nonlinear properties of complex natural phenomena, the evolution
of the quantity of interest can be often represented by systems of coupled
nonlinear stochastic differential equations (SDEs). These SDEs typically
contain several parameters which have to be chosen carefully to match the
experimental data and to validate the effectiveness of the model. In the
present paper the calibration of these parameters is described by nonlinear
SDE-constrained optimization problems. In the optimize-before-discretize
setting a rigorous analysis is carried out to ensure the existence of optimal
solutions and to derive necessary first-order optimality conditions. For the
numerical solution a Monte-Carlo method is applied using parallelization
strategies to compensate for the high computational time. In the numerical
examples an Ornstein-Uhlenbeck and a stochastic Prandtl-Tomlinson bath model
are considered.
