Related papers: Wavelet series representation for multifractional …
We present a multiscale description of hydrodynamic turbulence in incompressible fluid based on a continuous wavelet transform (CWT) and a stochastic hydrodynamics formalism. Defining the stirring random force by the correlation function of…
Rough paths techniques give the ability to define solutions of stochastic differential equations driven by signals $X$ which are not semimartingales and whose $p$-variation is finite only for large values of $p$. In this context, rough…
A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…
The infinitesimal generator of a one-dimensional strictly $\alpha$-stable process can be represented as a weighted sum of (right and left) Riemann-Liouville fractional derivatives of order $\alpha$ and one obtains the fractional Laplacian…
Implicit neural representations (INRs) have arisen as useful methods for representing signals on Euclidean domains. By parameterizing an image as a multilayer perceptron (MLP) on Euclidean space, INRs effectively represent signals in a way…
The suboptimal performance of wavelets with regard to the approximation of multivariate data gave rise to new representation systems, specifically designed for data with anisotropic features. Some prominent examples of these are given by…
This paper uses the invariance principle to solve the incidental parameter problem of [Econometrica 16 (1948) 1--32]. We seek group actions that preserve the structural parameter and yield a maximal invariant in the parameter space with…
We introduce a construction of multiscale tight frames on general domains. The frame elements are obtained by spectral filtering of the integral operator associated with a reproducing kernel. Our construction extends classical wavelets as…
Multivariate processes with long-range dependent properties are found in a large number of applications including finance, geophysics and neuroscience. For real data applications, the correlation between time series is crucial. Usual…
A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…
We develop and analyze a random field model for the reconstruction of turbulent velocity fluctuations from inhomogeneous characteristic flow quantities provided by RANS simulations that is accessible to both a rigorous analytical validation…
A multilevel Monte Carlo (MLMC) method for quantifying model-form uncertainties associated with the Reynolds-Averaged Navier-Stokes (RANS) simulations is presented. Two, high-dimensional, stochastic extensions of the RANS equations are…
Studying sample path behaviour of stochastic fields/processes is a classical research topic in probability theory and related areas such as fractal geometry. To this end, many methods have been developed since a long time in Gaussian…
A stochastic wavevector approach is formulated to accurately represent compressible turbulence subject to rapid deformations. This approach is inspired by the incompressible particle representation model of Kassinos (1995) and preserves the…
In this paper we obtain a martingale representation theorem in the progressive enlargement $\mathbb{G}$ by a random time $\tau$ of the filtration $\mathbb{F}^L$ generated by a L\'evy process $L$. The assumptions on the random time are that…
Due to complex physical phenomena, the distribution of heavy rainfall events is difficult to model spatially. Physically based numerical models can often provide physically coherent spatial patterns, but may miss some important…
We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods…
We numerically investigate a mean-field Bayesian approach with the assistance of the Markov chain Monte Carlo method to estimate motion velocity fields and probabilistic models simultaneously in consecutive digital images described by…
We present a new framework for robust estimation and inference on second-order stationary time series and random fields. This framework is based on the Generalized Method of Wavelet Moments which uses the wavelet variance to achieve…