A Correction to "Dynkin Games Via Dirichlet Forms and Singular Control of One-Dimensional Diffusion"

Abstract

In the paper "Dynkin Games Via Dirichlet Forms and Singular Control of One-Dimensional Diffusion", the authors tried to show the existences of a smooth value function and an optimal policy to a one-dimensional stochastic singular control problem, where the underlying process is a generalized diffusion process given by dX_t=μ(X_t)dt+σ(X_t)dw_t, in which w_t is a Wiener process. It is found that either a condition on μ(x) and σ(x) should be added, or a different diffusion process should be considered and as a result, the main theorem of this paper should be amended.

arXiv commentThis paper has been withdrawn. The content of this paper has been added to the appendix of the author's another paper 'A Multi-dimensional Stochastic Singular Control Problem Via Dynkin Game and Dirichlet Form'