Cadlag Skorokhod problem driven by a maximal monotone operator

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 $\Pi$, 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.

42 pages

References in corpus (2)

• Penalization methods for the Skorokhod problem and reflecting SDEs with jumps
• Sweeping processes with stochastic perturbations generated by a fractional Brownian motion

Cited by in corpus (1)

• On the continuity of the probabilistic representation of a semilinear Neumann-Dirichlet problem