A survey on cylindrical Levy processes in Banach spaces
主 题: A survey on cylindrical Levy processes in Banach spaces
报告人: Dr. Markus Riedle （ Dept of Mathematics King's College, London (UK)）
时 间: 2012-04-19 16:00-17:00
地 点: 理科一号楼1114
The objective of this talk is the introduction of cylindrical Levy processes and their stochastic integrals in Hilbert and Banach spaces.
The degree of freedom of models in infinite dimensions is often reflected by the request that each mode along a dimension is independently perturbed by the noise. In the Gaussian setting, this leads to the cylindrical Wiener process including from a model point of view the very important possibility to model a Gaussian noise in both time and space in a great flexibility (space-time white noise). Up to very recently, there has been no analogue for Levy processes.
Based on the theory of cylindrical processes and cylindrical measures we introduce cylindrical Levy processes as a natural generalisation of cylindrical Wiener processes. We continue to characterise the distribution of cylindrical Levy processes by a cylindrical version of the Levy-Khintchine formula.