A Theory of Generalized Random Processes and Its Applications,
TEXAS UNIV AUSTIN APPLIED MECHANICS RESEARCH LAB
Pagination or Media Count:
A class of generalized random processes is defined in the framework of vector-valued distributions or vector-valued generalized functions. Namely, a generalized random process in this class is a continuous linear transformation from a topological vector space of measuring test functions to a Banach space of random variables. A theory of the generalized random processes is developed based on the well developed work on the generalized functions. The generalized random process is an extended notion of a generalized function, and all generalized functions belong to the class of generalized random processes. Two sequences of spaces of generalized random processes are defined on the Sobolev spaces of measuring functions in two different ways. The so-called white Gaussian process is characterized in the framework of generalized random processes. The theory of generalized random processes developed here is applied to the estimation problems which involve the white Gaussian process or white process.
- Statistics and Probability