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Generating Sparse Stochastic Processes Using Matched Splines

Related publications (28)

Normal approximation of the solution to the stochastic heat equation with Levy noise

Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

SPRINGER2020

Support and approximation properties of Hermite splines

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Shayan Aziznejad

In this paper, we formally investigate two mathematical aspects of Hermite splines that are relevant to practical applications. We first demonstrate that Hermite splines are maximally localized, in the sense that the size of their support is minimal among ...

2020

Dictionary Learning for Two-Dimensional Kendall Shapes

Michaël Unser, Julien René Pierre Fageot, Virginie Sophie Uhlmann, Anna You-Lai Song

We propose a novel sparse dictionary learning method for planar shapes in the sense of Kendall, namely configurations of landmarks in the plane considered up to similitudes. Our shape dictionary method provides a good trade-off between algorithmic simplici ...

SIAM PUBLICATIONS2020

Wavelet analysis of the Besov regularity of Levy white noise

Julien René Pierre Fageot, Shayan Aziznejad

We characterize the local smoothness and the asymptotic growth rate of the Levy white noise. We do so by characterizing the weighted Besov spaces in which it is located. We extend known results in two ways. First, we obtain new bounds for the local smoothn ...

2020

Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems

Daniel Maria Busiello, Amos Maritan, Deepak Gupta

A general framework to describe a vast majority of biology-inspired systems is to model them as stochastic processes in which multiple couplings are in play at the same time. Molecular motors, chemical reaction networks, catalytic enzymes, and particles ex ...

2020

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Max-Olivier Hongler, Roger Filliger

We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...

Springer2019

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

Pablo Antolin Sanchez

3D objects, modeled using Computer Aided Geometric Design (CAGD) tools, are traditionally represented using a boundary representation (B-rep), and typically use spline functions to parameterize these boundary surfaces. However, recent development in physic ...

2019

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Michaël Unser, Julien René Pierre Fageot

Consider a random process s that is a solution of the stochastic differential equation Ls = w with L a homogeneous operator and w a multidimensional Levy white noise. In this paper, we study the asymptotic effect of zooming in or zooming out of the process ...

2019

Domain-Informed Spline Interpolation

Dimitri Nestor Alice Van De Ville, Zafer Dogan, Hamid Behjat

Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to different brain ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Generating Sparse Stochastic Processes Using Matched Splines

Normal approximation of the solution to the stochastic heat equation with Levy noise

Support and approximation properties of Hermite splines

Dictionary Learning for Two-Dimensional Kendall Shapes

Wavelet analysis of the Besov regularity of Levy white noise

Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Domain-Informed Spline Interpolation

Graph Chatbot

Normal approximation of the solution to the stochastic heat equation with Levy noise

Support and approximation properties of Hermite splines

Dictionary Learning for Two-Dimensional Kendall Shapes

Wavelet analysis of the Besov regularity of Levy white noise

Coarse-grained entropy production with multiple reservoirs: Unraveling the role of time scales and detailed balance in biology-inspired systems

On Jump-Diffusive Driving Noise Sources: Some Explicit Results and Applications

Volumetric untrimming: Precise decomposition of trimmed trivariates into tensor products

Scaling Limits of Solutions of Linear Stochastic Differential Equations Driven by Levy White Noises

Domain-Informed Spline Interpolation

The sources of sovereign risk: a calibration based on Levy stochastic processes

The sources of sovereign risk: a calibration based on Levy stochastic processes