Zobrazeno 1 - 10
of 203
pro vyhledávání: '"PODGÓRSKI, KRZYSZTOF"'
Deriving properties of excursion time distributions of stochastic processes is vital in many fields, such as physics and engineering. However, obtaining analytical results is difficult for most processes. A common approximation method in physics is t
Externí odkaz:
http://arxiv.org/abs/2410.06000
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distribution of the time in these states may differ. In this sense, the process is asymmetric, and this paper extends previou
Externí odkaz:
http://arxiv.org/abs/2409.05641
In physics and engineering literature, the distribution of the excursion-above-zero time distribution (exceedance distribution) for a stationary Gaussian process has been approximated by a stationary switching process with independently distributed s
Externí odkaz:
http://arxiv.org/abs/2401.01805
Functional data analysis is typically performed in two steps: first, functionally representing discrete observations, and then applying functional methods to the so-represented data. The initial choice of a functional representation may have a signif
Externí odkaz:
http://arxiv.org/abs/2309.16402
Autor:
Nassar, Hiba, Podgórski, Krzysztof
Periodic splines are a special kind of splines that are defined over a set of knots over a circle and are adequate for solving interpolation problems related to closed curves. This paper presents a method of implementing the objects representing such
Externí odkaz:
http://arxiv.org/abs/2302.07552
In implementations of the functional data methods, the effect of the initial choice of an orthonormal basis has not gained much attention in the past. Typically, several standard bases such as Fourier, wavelets, splines, etc. are considered to transf
Externí odkaz:
http://arxiv.org/abs/2103.07453
Autor:
Podgórski, Krzysztof
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it splinets} and
Externí odkaz:
http://arxiv.org/abs/2102.00733
This work is to popularize the method of computing the distribution of the excursion times for a Gaussian process that involves extended and multivariate Rice's formula. The approach was used in numerical implementations of the high-dimensional integ
Externí odkaz:
http://arxiv.org/abs/2007.14220
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the statistical distribu
Externí odkaz:
http://arxiv.org/abs/1911.07061
A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them. For this
Externí odkaz:
http://arxiv.org/abs/1910.07341