Filtering for fractional stochastic heat equation

Abstract

Linear ltering problem for innite-dimensional Gaussian processes with nite - dimensional observation process is studied. Integral equations for the lter and for covariance of the error are derived.

General results are applied to a stochastic evolution equation driven by cylindrical fractional Brownian motion observed at nitely many points on an unbounded domain.

Keywords

• Kalman - Bucy filter
• Stochastic evolution equations
• Gaussian processes
• heat equation