Stochastic systems with applications to Biology and Finance

这个项目与随机系统有关。这些受统计不确定性和可变性控制的数学系统在生物学和金融学领域具有深远的重要性。它们在世界范围内被认为具有重要的科学意义。需要研究的重要问题是：1)DNA聚合酶链反应中的分支过程，2)亚稳态系统中的长期平稳性，以及3)金融中的随机波动性。这些问题的答案将为各自领域的潜在突破奠定统计理论的基础。该项目将有助于随机过程的理论和应用，以及生物学和金融学的建模。

This project is concerned with stochastic systems. These mathematical systems, which are controlled by statistical uncertainty and variability, have profound importance in the fields of biology and finance. They are recognised worldwide as being of primary scientific importance. Important questions to be examined are: 1) Branching processes in DNA Polymerase Chain Reaction, 2) long term stationarity in metastable systems, and 3) Stochastic Volatility in Finance. The answers to these questions will underpin the statistical theory for potential breakthroughs in the respective areas. This project will contribute to the theory and applications of Stochastic Processes, as well as modelling in biology and finance.