Numerical schemes for multivalued backward stochastic differential systems
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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:
where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (Xt)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 inequality in conjunction with Yosida approximation techniques.
$$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$
KeywordsEuler scheme Yosida approximation Error estimate Multivalued backward SDEs Reflected SDEs
MSC65C99 60H30 47H15
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