Related papers: On forward-backward SDE approaches to continuous-t…
Taking a deterministic viewpoint this work investigates extensions of the Kalman-Bucy filter for state reconstruction to systems containing parametric uncertainty in the state operator. The emphasis lies on risk averse designs reducing the…
We investigate the optimal reinsurance problem under the criterion of maximizing the expected utility of terminal wealth when the insurance company has restricted information on the loss process. We propose a risk model with claim arrival…
We consider optimal signalling and control of discrete-time nonlinear partially observable stochastic systems in state space form. In the first part of the paper, we characterize the operational {\it control-coding capacity}, $C_{FB}$ in…
Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional…
This paper studies a nonlinear filtering problem over an infinite time interval. The signal to be estimated is driven by a stochastic partial differential equation involves unknown parameters. Based on discrete observation, strongly…
A dual control problem is presented for the optimal stochastic control of a system governed by partial differential equations. Relationships between the optimal values of the original and the dual problems are investigated and two duality…
This paper studies the problem of developing computationally efficient solutions for steering the distribution of the state of a stochastic, linear dynamical system between two boundary Gaussian distributions in the presence of…
The Kalman filter combines forecasts and new observations to obtain an estimation which is optimal in the sense of a minimum average quadratic error. The Kalman filter has two main restrictions: (i) the dynamical system is assumed linear…
We study backward stochastic differential equations (BSDEs) for time-changed L\'evy noises when the time-change is independent of the L\'evy process. We prove existence and uniqueness of the solution and we obtain an explicit formula for…
We investigate the problem of persistently monitoring a finite set of targets with internal states that evolve with linear stochastic dynamics using a finite set of mobile agents. We approach the problem from the infinite-horizon…
The Kalman filter is an established tool for the analysis of dynamic systems with normally distributed noise, and it has been successfully applied in numerous application areas. It provides sequentially calculated estimates of the system…
This paper investigates waveform estimation (tracking) of the time-varying force in a two-level optomechanical system with backaction noise by Kalman filtering. It is assumed that the backaction and measurement noises are Gaussian and…
We present results on parameter estimation and non-parameter estimation of the linear partially observed Gaussian system of stochastic differential equations. We propose new one-step estimators which have the same asymptotic properties as…
Author's Summary of the dissertation for the degree of the Candidate of Science (physics and mathematics). The aim of the dissertation is to develop a generalized Kalman Duality concept applicable for linear unbounded non-invertible…
We formulate a recursive estimation problem for multiple dynamical systems coupled through a low dimensional stochastic input, and we propose an efficient sub-optimal solution. The suggested approach is an approximation of the Kalman filter…
We propose an optimization formulation for the simultaneous estimation of a latent variable and the identification of a linear continuous-time dynamic system, given a single input-output pair. We justify this approach based on Bayesian…
Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…
In this paper, we consider a stochastic decision problem for a system governed by a stochastic differential equation, in which an optimal decision is made in such a way to minimize a vector-valued accumulated cost over a finite-time horizon…
The choice of the location of controllers and observations is of great importance for designing control systems and improving the estimations in various practical problems. For time-varying systems in Hilbert spaces, the existence and…
Reliable state estimation depends on accurately modeled noise covariances, which are difficult to determine in practice. This paper formulates the noise covariance estimation as a bilevel optimization problem that factorizes the joint…