This paper develops a theoretical framework for modeling limit order book dynamics in liquid markets characterized by high-frequency order submissions. The authors establish a functional central limit theorem that describes the joint evolution of bid and ask queues, demonstrating that when order arrival frequencies are sufficiently high, the complex intraday dynamics can be effectively approximated by a Markovian jump-diffusion process. This approximation operates in the positive orthant and its characteristics are explicitly derived from the statistical properties of the underlying order flow, providing a mathematically tractable representation of market microstructure behavior.

The significance of this result lies in its ability to generate analytical approximations for various quantities of practical interest to market participants and researchers, including the probability of price movements and the distribution of durations between price changes, conditional on the current state of the order book. The framework's generality allows it to accommodate a wide range of distributional assumptions and temporal dependence patterns in order flow, making it applicable to numerous stochastic models commonly used in market microstructure research, such as Poisson point processes, self-exciting point processes, and ACD-GARCH family models.