Identification of a hereditary system with distributed delay

We study the identification problem that arises in a linear hereditary system with distributed delay. This involves estimating an infinite-dimensional parameter and we use the method of sieves, proposed by Grenander, to solve this problem

A new martingale approach to Kalman Filtering

A new derivation of continuous-time Kalman Filter equations is presented. The underlying idea has been previously used to derive the smoothing equations. A unified approach to filtering and smoothing problems has thus been achieved

Boundary value processes: estimation and identification

Recent results obtained for boundary value processes and the associated smoothing and identification problems are presented in this paper. Both lumped and distributed parameter models are considered. Some open problems are discussed and the fundamental mathematical difficulties that arise in studying nonlinear extensions of the proposed models are mentioned

A martingale approach to state estimation in delay-differential systems

A rigorous derivation of filtering arid smoothing equations for linear stochastic systems with time delay is presented. The estimation equations are obtained in term of the innovation process of the problem under consideration. The method used is based on a representation theorem on Gaussian martingales

Control of linear stochastic time delayed systems

The linear-quadratic control problem of stochastic time-delayed systems has been solved using function space method. The solution demonstrates directly that the “separation theorem” holds for such systems

White noise theory of robust nonlinear filtering with correlated state and observation noises

In the direct white noise theory of nonlinear filtering, the state process is still modeled as a Markov process satisfying an Ito stochastic differential equation, while a finitely additive white noise is used to model the observation noise. In the present work, this asymmetry is removed by modeling the state process as the solution of a (stochastic) differential equation with a finitely additive white noise as the input. This makes it possible to introduce correlation between the state and observation noise, and to obtain robust nonlinear filtering equations in the correlated noise cas

Filtering and identification of stochastic volatility for parabolic type factor models

We consider the dynamics of forward rate process which is modeled by a parabolic type infinite-dimensional factor model with stochastic volatility. The parameters included in the stochastic volatility dynamics are estimated from the factor process as the observation data. Based on the maximum likelihood technique, we propose the off-line identification scheme and provide some numerical examples

Team decision theory for linear continuous-time systems

This paper develops a team decision theory for linear-quadratic (LQ) continuous-time systems. First, a counterpart of the well-known result of Radner on quadratic static teams is obtained for two-member continuous-time LQ static team problems when the statistics of the random variables involved are not necessarily Gaussian. An iterative convergent scheme is developed, which in the limit yields the optimal team strategies. For the special case of Gaussian distributions, the team-optimal solution is affine in the information available to each DM, and for the further special case when the team cost function does not penalize the intermediate values of state, the optimal strategies can be obtained by solving a Liapunov type time-invariant matrix equation. This static theory is then extended to LQG continuous-time dynamic teams with sampled observations under the one-step-delay observation sharing pattern. The unique solution is again affine in the information available to each DM, and further, it features a certainty-equivalence property