کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1155941 | 958787 | 2009 | 20 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Representations of the optimal filter in the context of nonlinear filtering of random fields with fractional noise Representations of the optimal filter in the context of nonlinear filtering of random fields with fractional noise](/preview/png/1155941.png)
The problem of nonlinear filtering of multiparameter random fields, observed in the presence of a long-range dependent spatial noise, is considered. When the observation noise is modelled by a persistent fractional Wiener sheet, several pathwise representations of the optimal filter are derived. The representations involve series of multiple stochastic integrals of different types and are particularly important since the evolution equations, satisfied by the best mean-square estimate of the signal random field, have a complicated analytical structure and fail to be proper (measure-valued) stochastic partial differential equations. Several of the above optimal filter representations involve a new family of strong martingale transforms associated to the multiparameter fractional Brownian sheet; the latter martingale family is of independent interest in fractional stochastic calculus of multiparameter random fields.
Journal: Stochastic Processes and their Applications - Volume 119, Issue 8, August 2009, Pages 2481–2500