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Numerical schemes for multivalued backward stochastic differential systems

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Central European Journal of Mathematics

Abstract

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:

$$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$

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 inequality in conjunction with Yosida approximation techniques.

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Authors and Affiliations

  1. Faculty of Mathematics, Alexandru Ioan Cuza University, Carol I Blvd. 9, Iaşi, 700506, Romania

    Lucian Maticiuc & Eduard Rotenstein

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  1. Lucian Maticiuc
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  2. Eduard Rotenstein
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Correspondence to Lucian Maticiuc.

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Maticiuc, L., Rotenstein, E. Numerical schemes for multivalued backward stochastic differential systems. centr.eur.j.math. 10, 693–702 (2012). https://doi.org/10.2478/s11533-011-0131-y

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  • DOI: https://doi.org/10.2478/s11533-011-0131-y

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