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When and how an error yields a Dirichlet form

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
240
Issue
2
Identifiers
DOI: 10.1016/j.jfa.2006.03.007
Keywords
  • Error
  • Approximation
  • Dirichlet Form
  • Square Field Operator
  • Bias
  • Wiener Space
  • Stochastic Differential Equation

Abstract

Abstract We consider a random variable Y and approximations Y n , n ∈ N , defined on the same probability space with values in the same measurable space as Y. We are interested in situations where the approximations Y n allow to define a Dirichlet form in the space L 2 ( P Y ) where P Y is the law of Y. Our approach consists in studying both biases and variances. The article attempts to propose a general theoretical framework. It is illustrated by several examples.

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