Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency NASDAQ100 tick data. Employing a discrete-time Markov chain framework, we categorize consecutive price changes into nine states and estimate transition probability matrices (TPMs) for six intraday intervals across High ($\mathtt{HMC}$), Medium ($\mathtt{MMC}$), and Low ($\mathtt{LMC}$) market cap stocks. Element-wise TPM comparison reveals systematic patterns: price inertia peaks during opening and closing hours, stabilizing midday. A capitalization gradient is observed: $\mathtt{HMC}$ stocks exhibit the strongest inertia, while $\mathtt{LMC}$ stocks show lower stability and wider spreads. Markov metrics, including spectral gap, entropy rate, and mean recurrence times, quantify these dynamics. Clustering analysis identifies three distinct temporal phases on the bid side -- Opening, Midday, and Closing, and four phases on the ask side by distinguishing Opening, Midday, Pre-Close, and Close. This indicates that sellers initiate end-of-day positioning earlier than buyers. Stationary distributions show limit order dynamics are dominated by neutral and mild price changes. Jensen-Shannon divergence confirms the closing hour as the most distinct phase, with capitalization modulating temporal contrasts and bid-ask asymmetry. These findings support capitalization-aware and time-adaptive execution algorithms.

翻译：定量理解限价单价格变动的随机动态对于执行策略设计至关重要。我们利用高频NASDAQ100逐笔数据，分析了不同市值层级上卖单和买单的日内转移动态。采用离散时间马尔可夫链框架，我们将连续价格变动划分为九种状态，并针对高市值($\mathtt{HMC}$)、中市值($\mathtt{MMC}$)和低市值($\mathtt{LMC}$)股票，在六个日内时间区间内估计了转移概率矩阵。逐元素的TPM比较揭示了系统性模式：价格惯性在开盘和收盘时段达到峰值，并在午盘时段趋于稳定。观察到市值梯度效应：$\mathtt{HMC}$股票表现出最强的惯性，而$\mathtt{LMC}$股票稳定性较低且价差更宽。包括谱隙、熵率和平均重现时间在内的马尔可夫度量量化了这些动态。聚类分析在买单侧识别出三个不同的时间阶段——开盘、午盘和收盘，在卖单侧则通过区分开盘、午盘、收盘前和收盘识别出四个阶段。这表明卖方比买方更早启动日终头寸调整。稳态分布显示限价单动态主要由中性及温和的价格变动主导。Jensen-Shannon散度证实收盘时段是最具区分度的阶段，市值调节了时间对比度及买卖价差不对称性。这些发现支持了考虑市值因素且时间自适应的执行算法。