Remarks on a controlled degenerate diffusion process

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We establish explicit estimates for a two-dimensional LQG homing problem with a zero terminal cost under the assumption that the controlled diffusion process is degenerate. The present results extend and complete those in Lefebvre (2013) which are given explicitly for a particular interesting case. Our main tool is a nonlinear integral inequality of the Gronwall type. As an application, we consider a simple example to illustrate the present results.