  In this paper, we consider the product-limit quantile estimator of an unknown
quantile function under a censored dependent model. This is a parallel problem
to the estimation of the unknown distribution function by the product-limit
estimator under the same model. Simultaneous strong Gaussian approximations of
the product-limit process and product-limit quantile process are constructed
with rate $O((\log n)^{-\lambda})$ for some $\lambda>0,$. The strong Gaussian
approximation of the product-limit process is then applied to derive the laws
of the iterated logarithm for product-limit process.
