Related papers: Linear Filtering for Discrete Time Systems Driven …
A method is proposed to generate an optimal fit of a number of connected linear trend segments onto time-series data. To be able to efficiently handle many lines, the method employs a stochastic search procedure to determine optimal…
In the paper, we consider nonlinear filtering problems of multiscale systems in two cases-correlated sensor L\'evy noises and correlated L\'evy noises. First of all, we prove that the slow part of the origin system converges to the…
Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise.…
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…
This paper is concerned with a problem of robust filtering for a finite-dimensional linear discrete time invariant system with two output signals, one of which is directly observed while the other has to be estimated. The system is assumed…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…
In the context of track fitting problems by a Kalman filter, the appropriate functional forms of the elements of the random process noise matrix are derived for tracking through thick layers of dense materials and magnetic field. This work…
The paper studies the problem of filtering a discrete-time linear system observed by a network of sensors. The sensors share a common communication medium to the estimator and transmission is bit and power budgeted. Under the assumption of…
We analyze the quantum dynamics of radiation propagating in a single mode optical fiber with dispersion, nonlinearity, and Raman coupling to thermal phonons. We start from a fundamental Hamiltonian that includes the principal known…
We consider stochastic non-linear diffusion equations with a highly singular diffusivity term and multiplicative gradient-type noise. We study existence and uniqueness of non-negative variational solutions in terms of stochastic variational…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
Discretizing continuous-time linear systems typically requires numerical integration. This document presents a convenient method for discretizing the dynamics, input, and process noise state-space matrices of a continuous-time linear system…
We consider multiscale stochastic systems that are partially observed at discrete points of the slow time scale. We introduce a particle filter that takes advantage of the multiscale structure of the system to efficiently approximate the…
We consider a class of linear Vlasov partial differential equations driven by Wiener noise. Different types of stochastic perturbations are treated: additive noise, multiplicative It\^o and Stratonovich noise, and transport noise. We…
Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…
We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…
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 consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
We introduce a weighted particle representation for the solution of the filtering problem based on a suitably chosen variation of the classical de Finetti theorem. This representation has important theoretical and numerical applications. In…
We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. Firstly, we prove that the dimension for the signal system can be reduced by a homogenized approach. Secondly,…