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We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality: $$d{Y}_t+F(t,X_t,Y_t,Z_t)dt\in \partial \phi \left(Y_t\right)dt+Z_{t}d{W}_t,$$ where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t)t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational...

Our aim is to study the following new type of multivalued backward stochastic differential equation: $$\left\{\begin{array}{c}-dY\left(t\right)+\partial \phi \left(Y\left(t\right)\right)dt\ni F\left(t,Y\left(t\right),Z\left(t\right),Y_t,Z_t\right)dt+Z\left(t\right)dW\left(t\right),0⩽t⩽T,\\ Y\left(T\right)=\xi ,\end{array}\right.$$ where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.