Related papers: Parameter Estimation for Jump-Diffusion Stochastic…
Estimating parameters of a diffusion process given continuous-time observations of the process via maximum likelihood approaches or, online, via stochastic gradient descent or Kalman filter formulations constitutes a well-established…
A finite-dimensional Markovian open quantum system will undergo quantum jumps between pure states, if we can monitor the bath to which it is coupled with sufficient precision. In general these jumps, plus the between-jump evolution, create…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
The estimation of the density matrix of a $k$-level quantum system is studied when the parametrization is given by the real and imaginary part of the entries and they are estimated by independent measurements. It is established that the…
The master equation for the state of an open quantum system can be unravelled into stochastic trajectories described by a stochastic master equation. Such stochastic differential equations can be interpreted as an update formula for the…
The coefficients in a second order parabolic linear stochastic partial differential equation (SPDE) are estimated from multiple spatially localised measurements. Assuming that the spatial resolution tends to zero and the number of…
Measuring stochastic signals ("noise metrology") constitutes a central task in quantum sensing and the characterization of open quantum systems. Here we establish ultimate precision bounds for multiparameter estimation of stochastic signals…
Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for…
We present a quantum algorithm to estimate parameters at the quantum metrology limit using deterministic quantum computation with one bit. When the interactions occurring in a quantum system are described by a Hamiltonian $H= \theta H_0$,…
Memory or time-non-local effects in open quantum dynamics pose theoretical as well as practical challenges in the understanding and control of noisy quantum systems. While there has been a comprehensive and concerted effort towards…
In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Stochastic Partial Differential Equations (SPDEs) driven by random noise play a central role in modeling physical processes with rough spatio-temporal dynamics, such as turbulence flows, superconductors, and quantum dynamics. Although…
Currently, there is no general theory for deriving diffusion approximations of queueing systems with high- or infinite-dimensional state descriptors. In this paper, we explore one path for deriving diffusion limit equations of queueing…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
We derive stochastic master equation for a quantum system interacting with an environment prepared in a continuous-mode $N$-photon state. To determine the conditional evolution of the quantum system depending on continuous in time…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
Two types of random evolution processes are studied for ensembles of the standard map with driving parameter $K$ that determines its degree of stochasticity. For one type of processes the parameter $K$ is chosen at random from a Gaussian…
In this paper we investigate quasi-stationary distributions {\mu}_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological…
This paper re-examines the problem of parameter estimation in Bayesian networks with missing values and hidden variables from the perspective of recent work in on-line learning [Kivinen & Warmuth, 1994]. We provide a unified framework for…