Cadlag Skorokhod problem driven by a maximal monotone operator (1306.1686v2)

Abstract: The article deals with existence and uniqueness of the solution of the following differential equation (a c`adl`ag Skorokhod problem) driven by a maximal monotone operator and with singular input generated by the c`{a}dl`{a}g 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 $\Pi$, by taking $x_{t}=\Pi(x_{t-}+\Delta m_{t})$, whenever $x_{t-}+\Delta m_{t}\notin\overline {\mathrm{D}(A)}\,$. Approximations of the solution based on discretization and Yosida penalization are considered.