Cameron-Martin space
Definition 1.
Let be Wiener space. The Cameron-Martin space is the subspace of consisting of all paths such that is absolutely continuous and . (Note that if is absolutely continuous, then it is almost everywhere differentiable
, so the integral makes sense.)
This can be thought of as the set of paths with “finite energy.”
Note that has Wiener measure , since sample paths of Brownian motion are nowhere differentiable, whereas a path from is almost everywhere differentiable.
Title | Cameron-Martin space |
---|---|
Canonical name | CameronMartinSpace |
Date of creation | 2013-03-22 15:55:56 |
Last modified on | 2013-03-22 15:55:56 |
Owner | neldredge (4974) |
Last modified by | neldredge (4974) |
Numerical id | 6 |
Author | neldredge (4974) |
Entry type | Definition |
Classification | msc 60H99 |
Related topic | WienerMeasure |
Defines | Cameron-Martin space |