Infinite-Dimensional Filtering

摘要: This paper presents a generalization of the standard Kalman–Bucy linear filtering problem to infinite dimensions. The infinite-dimensional stochastic dynamical system is represented as evolution equation \[du(t,\omega ) = \mathcal{A}(t)u(t,\omega )dt + \mathcal{B}(t)dw(t,\omega ),\] where $A(t)$ an unbounded operator, $\mathcal{B}(t)$ bounded $w(t,\omega )$ Hilbert space-valued Wiener process and $u(t,\omega then process. observation by \[dz(t,\omega \mathcal{C}(t)u(t,\omega \mathcal{F}(t)dv(t,\omega $\mathcal{C}(t)$ $\mathcal{F}(t)$ are operators $v(t)$ finite-dimensional Using combination techniques abstract probability theory, existence optimal filter for based on $z(t,\omega )$, $0 \leqq s t$, established. As in may be...