State-space Representation of Matérn and Damped Simple Harmonic Oscillator Gaussian Processes
نویسندگان
چکیده
Gaussian processes (GPs) are used widely in the analysis of astronomical time series. GPs with rational spectral densities have state-space representations which allow O(n) evaluation likelihood. We calculate analytic state space for damped simple harmonic oscillator and Mat\'ern 1/2, 3/2 5/2 processes.
منابع مشابه
Kraus representation of a damped harmonic oscillator and its application
Yu-xi Liu, Șahin K. Özdemir, Adam Miranowicz, and Nobuyuki Imoto The Graduate University for Advanced Studies (SOKENDAI), Shonan Village, Hayama, Kanagawa 240-0193, Japan Frontier Research System, The Institute of Physical and Chemical Research (RIKEN), Wako-shi 351-0198, Japan SORST Research Team for Interacting Career Electronics, Hayama, Kanagawa 240-0193, Japan CREST Research Team for Photo...
متن کاملDamped Quantum Harmonic Oscillator
In the framework of the Lindblad theory for open quantum systems the damping of the harmonic oscillator is studied. A generalization of the fundamental constraints on quantum mechanical diffusion coefficients which appear in the master equation for the damped quantum oscillator is presented; the Schrödinger and Heisenberg representations of the Lindblad equation are given explicitly. On the bas...
متن کاملQuantum Damped Harmonic Oscillator Revisited
In this paper we revisit the quantum damped harmonic oscillator and construct an interesting approximate solution in the operator algebra level. Namely, we first give the general solution to the Lindblad form (equation) and next construct an approximate solution to the full equation by use of it. Our method is a milestone to construct the general solution. In this paper we revisit dynamics of a...
متن کاملQuantizing the damped harmonic oscillator
We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...
متن کاملState Space representation of non-stationary Gaussian Processes
The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where n is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS representation of the most important kernels used in machine learning. The aim ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Research notes of the AAS
سال: 2021
ISSN: ['2515-5172']
DOI: https://doi.org/10.3847/2515-5172/abfe68