In his study on the probability theory and as a founding figure in this field, Laplace demonstrated a method of deriving asymptotic approximations of integrals depending on a large parameter. Laplace’s method plays a central role in the probability theory as well as other disciplines. Kai Lai Chung considered such a probability problem in the late 1940s, which was solved in a work collaborating with Paul Erdös. Their approach was probabilistic and Chung would like to find a purely analytic one. The problem is to find the asymptotic approximation of a quotient of two Laplace integrals under a rather general condition -- an analytical problem in its own nature. Chung was curious about an analytic approach and announced this as an open problem twice, in 1954 and 1998. In this talk, we discuss a recent attempt to solve this problem.

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