Stochastic Process
§1 Introduction§§1.2 Kolmogorov Thm. and Separability1. Kolmogorov TheoremProposition: Suppose is a Polish space with a compatible probability measure family , then there is a probability on s.t. coincides with on finite rectangle parabolic set on . 2. SeparabilityDefinition: Separability of stochastic process: open interval , closed set , , , a.eIf is separable, then , a.e. -measurable. (), when 3. Shift OperatorDefinition: (Shift operator) Let , is closed under addition. Define...