A probabilistic approach to second order variational inequalities with bilateral constraints

We study a class of second order variational inequalities with bilateral constraints. Under certain conditions we show the existence of a unique viscosity solution of these variational inequalities and give a stochastic representation to this solution. As an application, we study a stochastic game with stopping times and show the existence of a saddle point equilibrium.

Mrinal K Ghosh, K S Mallikarjuna Rao · 2004