Article ID Journal Published Year Pages File Type
9495945 Journal of Functional Analysis 2005 11 Pages PDF
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 Γ-i.e. error structures-and we are looking for an object related to Γ 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 Γ. 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
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