Advertisement

Probability Measures on Functional Spaces

Chapter
  • 1.3k Downloads
Part of the Classics in Mathematics book series

Abstract

Kolmogorov’s theorem on the construction of a probability space from finite-dimensional distributions of a random process with values in a metric space ℋ shows, in particular, how to construct a measure μ on a measurable space (ℱ,ℬ) — where ℱis the space of all the functions with values in ℋ and ℬ is the minimal σ-algebra containing all the cylinders in ℱ,such that, for any cylinder C, the value μ(C) coincides with the probability that the sample function of the random process belongs to C. This measure is called the measure associated with (or corresponding to) the random process ξ(t)and it can always be constructed irrespective of the probability space on which the process ξ(t) is defined.

Keywords

Hilbert Space Probability Measure Functional Space Gaussian Measure Sample Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Institute of Applied Mathematics and MechanicsAcademy of Sciences of the Ukrainian SSRDonetskUSSR
  2. 2.Institute of MathematicsAcademy of Sciences of the Ukrainian SSRKievUSSR

Personalised recommendations