Stochastic variational inequalities with oblique subgradients (Q432510)
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scientific article; zbMATH DE number 6052940
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stochastic variational inequalities with oblique subgradients |
scientific article; zbMATH DE number 6052940 |
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Stochastic variational inequalities with oblique subgradients (English)
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4 July 2012
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oblique reflection
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Skorohod problem
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stochastic variational inequalities
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The authors study existence and uniqueness of a solution to the following stochastic variational inequality with oblique subgradients NEWLINE\[NEWLINE dX_{t}+H(X_{t})\partial \varphi(X_{t})\left( dt \right) \ni f\left( t, X_{t} \right) dt+g\left( t, X_{t} \right)dB_{t}. NEWLINE\]NEWLINE The interplay between monotonicity of the subdifferential operator \(\partial \varphi\) and the assumption on the matrix map \(X \mapsto H(X)\) of being Lipschitz, makes the setting more difficult than the classical case of stochastic variational inequalities. The existence result is based on solving a deterministic generalized Skorohod problem with oblique reflection first.
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