In this paper we introduce a consensus-based distributed filter, executed by a sensor network, inspired by the Markovian jump linear system filtering theory. We show that the optimal filtering gains of the Markovian jump linear system can be used as an approximate solution of the optimal distributed filtering problem. This parallel allows us to interpret each filtering gain corresponding to a m...

This paper provides an introduction to quantum filtering theory. An introduction to quantum probability theory is given, focusing on the spectral theorem and the conditional expectation as a least squares estimate, and culminating in the construction of Wiener and Poisson processes on the Fock space. We describe the quantum Itô calculus and its use in the modeling of physical systems. We use bo...

A central limit theorem for bilinear forms of the type aĈN (ρ) −1b, where a, b ∈ C are unit norm deterministic vectors and ĈN (ρ) a robust-shrinkage estimator of scatter parametrized by ρ and built upon n independent elliptical vector observations, is presented. The fluctuations of aĈN (ρ) −1b are found to be of order N− 1 2 and to be the same as those of aŜN (ρ) −1b for ŜN (ρ) a matrix of a th...

We calculate the non-linear matter power spectrum using the 3rd-order perturbation theory without ignoring the pressure gradient term. We consider a semi-realistic system consisting of two matter components with and without pressure, and both are expanded into the 3rd order in perturbations in a self-consistent manner, for the first time. While the pressured component may be identified with bar...

By extending the ltering theory under the (min; +)-algebra to the time varying setting, we solve the problem of constrained traac regulation and develop a calculus for dynamic service guarantees. For a constrained traac regulation problem with maximum tolerable delay d and maximum buuer size q, the optimal regulator that generates the output traac conforming to a subadditive envelope f and mini...

This paper describes DIVA, a decision-theoretic agent for recommending movies that contains a number of novel features. DIVA represents user preferences using pairwise comparisons among items, rather than numeric ratings. It uses a novel similarity measure based on the concept of the probability of conflict between two orderings of ̄ items. The system has a rich representation of preference, dis...

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The focus of this work is on a two-dimensional stochastic vorticity equation for an incompressible homogeneous viscous fluid. We consider a signed measure-valued stochastic partial differential equation for a vorticity process based on the Skorohod–Ito evolution of a system of N randomly moving point vortices. A nonlinear filtering problem associated with the evolution of the vorticity is consi...

We present a mean field particle theory for the numerical approximation of Feynman-Kac path integrals in the context of nonlinear filtering. We show that the conditional distribution of the signal paths given a series of noisy and partial observation data is approximated by the occupation measure of a genealogical tree model associated with mean field interacting particle model. The complete hi...