## A Matrix Equation Arising in Statistical Filter Theory, Volume 270 |

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ARISING IN STATISTICAL assumed asymptotically stable Bucy have shown coefficients A(t Corollary covariance matrix definite critical point E(t)-*S exponentially fast eigenvalues of F eigenvector equation 1-1 escape to infinity Ex(t F is stable f(SQ fast as t-*oo hermitian matrix hypothesis of Theorem identity matrix implies initial condition X(0 Let Y(t linear differential equation matrix quadratic matrix R-S matrix Riccati equation n-dimensional negative by regularity negative definite critical negative real Newton's method iteration non-negative real nonsingular null vector obtained by solving ordering and boundedness persistent critical point point of 1-1 point of equation positive definite positive semidefinite critical Proof of lemma regularity property satisfies the differential SBSe Schwartz distribution second moments semidefinite critical point side of equation singular solution E(t solution of 1-1 solution of equation stable matrix statistical problem leading steady state solution stochastic process Theorem 2-1 tilde version unstable mode verified by substitution