Cylindrical Levy Processes and Their Applications

圆柱征税流程及其应用

基本信息

批准号：
EP/I036990/1
负责人：
Markus Riedle
金额：
$ 12.81万
依托单位：
King's College London
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2012
资助国家：
英国
起止时间：
2012 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FI036990%2F1
关键词：
Cylindrical Levy Processes Their Applications

项目摘要

Stochastic differential equations model a process evolving in time and subject to a random noise. Numerous phenomena in nature and economics are modelled by these equations. The reason for the random noise might be found in external or internal fluctuations which do not allow a deterministic description, in random events in the future or in uncertainty of the model. The complexity of the model, e.g. the numbers of parameters involved or the state space of the modelled process, often results in the necessity to consider stochastic differential equations in infinite dimensional spaces. However, up to now, most of these models are restricted to a continuous Gaussian noise and to infinite dimensional spaces with a very rich structure due to the lack of a satisfactory mathematical theory.The first objective of this project is to develop a theory which enables us to treat stochastic differential equations in infinite dimensional spaces of a general type. The random source might have discontinuous paths and is allowed to be of a very general form, such that the randomness not only depends on the evolution in time but also on the underlying space. In the second part of this project, the usability of the theory is verified by studying two concrete examples out of the numerous applications: one model describes the physical distribution of the heat in a given region subject to some external random noise, and the second model originates from financial mathematics and describes the evolution of interest rate curves.

随机微分方程模拟随时间演变并受到随机噪声影响的过程。自然和经济中的许多现象都是通过这些方程来建模的。随机噪声的原因可能是无法进行确定性描述的外部或内部波动、未来的随机事件或模型的不确定性。模型的复杂性，例如所涉及的参数数量或建模过程的状态空间通常导致需要考虑无限维空间中的随机微分方程。然而，到目前为止，由于缺乏令人满意的数学理论，大多数这些模型都局限于连续高斯噪声和结构非常丰富的无限维空间。该项目的首要目标是发展一种理论，使我们处理一般类型的无限维空间中的随机微分方程。随机源可能具有不连续的路径，并且允许具有非常通用的形式，使得随机性不仅取决于时间的演化，还取决于底层空间。在该项目的第二部分中，通过研究众多应用中的两个具体示例来验证该理论的可用性：一个模型描述了受某些外部随机噪声影响的给定区域中热量的物理分布，第二个模型描述了特定区域中热量的物理分布。起源于金融数学，描述利率曲线的演变。