# Numerical schemes for multivalued backward stochastic differential systems

Open Mathematics (2012)

• Volume: 10, Issue: 2, page 693-702
• ISSN: 2391-5455

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## Abstract

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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: $d{Y}_{t}+F\left(t,{X}_{t},{Y}_{t},{Z}_{t}\right)dt\in \partial \phi \left({Y}_{t}\right)dt+{Z}_{t}d{W}_{t},$ 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 inequality in conjunction with Yosida approximation techniques.

## How to cite

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Lucian Maticiuc, and Eduard Rotenstein. "Numerical schemes for multivalued backward stochastic differential systems." Open Mathematics 10.2 (2012): 693-702. <http://eudml.org/doc/269491>.

@article{LucianMaticiuc2012,
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.},
author = {Lucian Maticiuc, Eduard Rotenstein},
journal = {Open Mathematics},
keywords = {Euler scheme; Yosida approximation; Error estimate; Multivalued backward SDEs; Reflected SDEs; error estimate; multivalued backward SDEs; reflected SDEs; Brownian motion; stochastic differential equations (SDEs)},
language = {eng},
number = {2},
pages = {693-702},
title = {Numerical schemes for multivalued backward stochastic differential systems},
url = {http://eudml.org/doc/269491},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Lucian Maticiuc
AU - Eduard Rotenstein
TI - Numerical schemes for multivalued backward stochastic differential systems
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 693
EP - 702
AB - 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.
LA - eng
KW - Euler scheme; Yosida approximation; Error estimate; Multivalued backward SDEs; Reflected SDEs; error estimate; multivalued backward SDEs; reflected SDEs; Brownian motion; stochastic differential equations (SDEs)
UR - http://eudml.org/doc/269491
ER -

## References

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