Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495945 | Journal of Functional Analysis | 2005 | 11 Pages |
Abstract
In order to develop a differential calculus for error propagation of Bouleau [Error Calculus for Finance and Physics, the Language of Dirichlet forms, De Gruyter, Berlin, 2003], we study local Dirichlet forms on probability spaces with carré du champ Î-i.e. error structures-and we are looking for an object related to Î which is linear and with a good behaviour by images. For this we introduce a new notion called the measure-valued gradient which is a randomized square root of Î. The exposition begins with inspecting some natural notions candidate to solve the problem before proposing the measure-valued gradient and proving its satisfactory properties.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Nicolas Bouleau,