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

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.

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