Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional Brownian sheet observation noise
| dc.creator | Amirdjanova, Anna | |
| dc.creator | Linn, Matthew | |
| dc.date | 2007-07-26 | |
| dc.date.accessioned | 2026-07-07T08:20:25Z | |
| dc.date.available | 2026-07-07T08:20:25Z | |
| dc.description | The problem of nonlinear filtering of a random field observed in the presence of a noise, modeled by a persistent fractional Brownian sheet of Hurst index $(H_1,H_2)$ with $0.5<H_1,H_2<1$, is studied and a suitable version of the Bayes' formula for the optimal filter is obtained. Two types of spatial "fractional" analogues of the Duncan-Mortensen-Zakai equation are also derived: one tracks evolution of the unnormalized optimal filter along an arbitrary "monotone increasing" (in the sense of partial ordering in $\mathbb{R}^2$) one-dimensional curve in the plane, while the other describes dynamics of the filter along the paths that are truly two-dimensional. Although the paper deals with the two-dimensional parameter space, the presented approach and results extend to $d$-parameter random fields with arbitrary $d\geq 3$. | |
| dc.description | 24 pages | |
| dc.identifier | https://arxiv.org/abs/0707.3856 | |
| dc.identifier | http://arxiv.org/abs/0707.3856 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135067 | |
| dc.subject | Probability | |
| dc.title | Stochastic evolution equations for nonlinear filtering of random fields in the presence of fractional Brownian sheet observation noise | |
| dc.type | text |