Parameter identification for deterministic and stochastic differential equations using the "collage method" for fixed point equations
A number of inverse problems may be viewed in terms of the approximation of a target element x in a complete metric space (X,d) by the fixed point x* of a contraction function T : X -> X. In practice, from a family of contraction functions T(a) one wishes to find the parameter a for which the approximation error d(x,x*(a)) is as small as possible. Thanks to a simple consequence of Banach's fixed point theorem known as the Collage Theorem, most practical methods of solving the inverse problem for fixed point equations seek to find an operator T(a) for which the so called collage distance d(x,T(a)x) is as small as possible. We first show how to solve inverse problems for deterministic and random differential equations and then we switch to the analysis of stochastic differential equations. Here inverse problems can be solved by minimizing the collage distance in an appropriate metric space. At the end we show an application of this approach to a system of coupled stochastic differential equations which describes the interaction between particles in a physical system
|Date of creation:||08 Apr 2008|
|Contact details of provider:|| Postal: Via Conservatorio 7, I-20122 Milan - Italy|
Phone: +39 02 50321522
Fax: +39 02 50321505
Web page: http://www.demm.unimi.it
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:mil:wpdepa:2008-08. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (DEMM Working Papers)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.