Details

Autor(en) / Beteiligte

• CLARK, J. M. C
• CRISAN, D

Titel

On a robust version of the integral representation formula of nonlinear filtering

Ist Teil von

• Probability theory and related fields, 2005-09, Vol.133 (1), p.43-56

Ort / Verlag

Heidelberg: Springer

Erscheinungsjahr

2005

Quelle

EBSCOhost Business Source Ultimate

Beschreibungen/Notizen

• The paper is concerned with completing "unfinished business" on a robust representation formula for the conditional expectation operator of nonlinear filtering. Such a formula, robust in the sense that its dependence on the process of observations is continuous, was stated in [2] without proof. The main purpose of this paper is to repair this deficiency. The formula is "almost obvious" as it can be derived at a formal level by a process of integration-by-parts applied to the stochastic integrals that appear in the integral representation formula. However, the rigorous justification of the formula is quite subtle, as it hinges on a measurability argument the necessity of which is easy to miss at first glance. The continuity of the representation (but not its validity) was proved by Kushner [9] for a class of diffusions. [PUBLICATION ABSTRACT]