.png){kind=icon}
.png){kind=icon}
Return
A computational introduction to random functions
.png){kind=icon}
PRE
AI
DOI：10.1007/s11075-026-02349-0.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
For readers working in applications, this paper serves as a basic primer for the numerical calculation of (pseudo-) random functions. Keeping probabilistic arguments at a minimum in favour of computation, random functions are studied by randomizing coefficients of expansions. This reveals a natural connection to Reproducing Kernel Hilbert spaces. Randomizing the coefficients of orthonormal Newton bases of Reproducing Kernel Hilbert spaces allows a comprehensive, constructive, and computational presentation, providing regularity results and error bounds in terms of variances. The approach is unexpectedly general, because paths of most random fields are shown to arise this way. A natural extension allows to use expansions in L-2 spaces, in particular wavelets and finite elements. Smoothing operators are introduced for the transition from white noise to random functions in higher-order Sobolev spaces, leading to algorithms without solving stochastic partial differential equations. Numerical examples serve for illustration.
Keywords:
Random generators
Kernel expansions
Sobolev spaces
Smoothing operators
Paths of random fields
Journal
N
IF:
2
Papers:
181
Citations:
5.5K