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一般化的费勒理论的分化
Christa Cuchiero1, Tonio Möllmann2, Josef Teichmann3
1Department of Statistics and Operations Research, Data Science @ Uni Vienna, Vienna University, Kolingasse 14-16 1, 1090 Wien, Austria.
概括
一般化的费勒理论将费勒理论扩展到非局部紧的空间,帮助随机微分方程和分数过程. 本研究详细介绍了结构,路径属性,并介绍了扩展的费勒过程.
科学领域:
- 可能性理论概率理论.
- 随机过程 随机过程
- 数学分析的数学分析
背景情况:
- 费勒理论是分析马尔科夫过程的基础,通常在局部紧的状态空间中.
- 一般化的费勒理论将这些概念扩展到更广泛的状态空间,这对于高级随机建模至关重要.
- 应用包括随机部分微分方程和特征随机微分方程.
研究的目的:
- 扩展和严格证明关于一般化的费勒过程的民间传说结果.
- 介绍和分析扩展费勒过程的新概念.
- 在加权空间上建立一般化费勒半组和微分方程之间的连接.
主要方法:
- 对一般化费勒过程的构造和路径属性的详细数学证明.
- 概括的费勒过程与经典的费勒过程和Doob的h变换进行比较分析.
- 应用特征方法将半组与传输方程和半流连接起来.
主要成果:
- 扩展和严格验证几个关键结果的一般化费勒过程.
- 引入扩展的费勒过程,为随机分析提供了一个新的框架.
- 通过费勒半组证明一种通用方法,通过费勒半组在加权空间上解决微分方程.
结论:
- 一般化的费勒理论是分析复杂的随机系统的强大工具.
- 新引入的扩展费勒工艺需要进一步研究.
- 一个反例证实了一般化的费勒半组定义中所有条件的必要性.
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