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arXiv · 1306.1686

Cadlag Skorokhod problem driven by a maximal monotone operator

Lucian Maticiuc·Aurel Răşcanu·Leszek Słomiński·Mateusz Topolewski
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Abstract

The article deals with existence and uniqueness of the solution of the following differential equation (a càdlàg Skorokhod problem) driven by a maximal monotone operator and with singular input generated by the càdlàg function $m$: \[ \left\{ \begin{array} [c]{l} dx_{t}+A\left( x_{t}\right) \left( dt\right) +dk_{t}^{d}\ni dm_{t} \,,~t\geq0,\\ x_{0}=m_{0}, \end{array} \right. \] where $k^{d}$ is a pure jump function. The jumps outside of the constrained domain $\overline{\mathrm{D}(A)}$ are counteracted through the generalized projection $Π$, by taking $x_{t}=Π(x_{t-}+Δm_{t})$, whenever $x_{t-}+Δm_{t}\notin\overline {\mathrm{D}(A)}\,$. Approximations of the solution based on discretization and Yosida penalization are considered.

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Lucian Maticiuc, Aurel Răşcanu, Leszek Słomiński, Mateusz Topolewski. 2015-03-02. Cadlag Skorokhod problem driven by a maximal monotone operator. https://doi.org/10.1016/j.jmaa.2015.03.086

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