中文摘要：

应用交互作用机制和统计物理方法，建立了描述同一证券市场中两支证券指数连锁反应的波动模型，用以研究两者之间存在交互反应的统计特性．借助于随机分析和双随机分离线模型探讨了证券连锁反应的概率分布，进而揭示出两支证券指数模型波动的概率测度的渐近性．同时讨论了交互作用下，单支证券指数波动的概率性质．最后对所建立金融模型的有限维概率分布收敛性进行了分析．

英文摘要：

Applying the theory of interacting systems and statistical physics, this paper establishes the fluctuations model for describing the chain reaction of two stock indices in a stock market in order to study the interacting reaction properties and the statistical properties of them. With the help of stochastic analysis and the two random paths model, the paper discusses the probability distribution for the chain reaction of stock indices, further it shows the asymptotical behavior of probability measures of the fluctuations for the two stock indices model. It also investigates the characters of single stock fluctuations by interacting reaction. Finally, it analyses the convergence of the finite dimensional prob- ability distributions for the financial model.