The Experts below are selected from a list of 53307 Experts worldwide ranked by ideXlab platform
Martin Ondrejat - One of the best experts on this subject based on the ideXlab platform.
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Invariant Measure for the stochastic navier stokes equations in unbounded 2d domains
Annals of Probability, 2017Co-Authors: Zdzislaw Brzeźniak, Elzbieta Motyl, Martin OndrejatAbstract:Building upon a recent work by two of the authors and J. Seidler on bwbw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an Invariant Measure to stochastic 2-D Navier–Stokes (with multiplicative noise) equations in unbounded domains. This answers an open question left after the first author and Y. Li proved a corresponding result in the case of an additive noise.
Arnaud Debussche - One of the best experts on this subject based on the ideXlab platform.
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An integral inequality for the Invariant Measure of a stochastic reaction--diffusion equation
Journal of Evolution Equations, 2017Co-Authors: Giuseppe Da Prato, Arnaud DebusscheAbstract:We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove an integral inequality for the Invariant Measure $\nu$ of a stochastic reaction--diffusion equation. Then we discuss some consequences as an integration by parts formula which extends to $\nu$ a basic identity of the Malliavin Calculus. Finally, we prove the existence of a surface Measure for a ball and a half-space of $H$.
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Invariant Measure of scalar first order conservation laws with stochastic forcing
Probability Theory and Related Fields, 2015Co-Authors: Arnaud Debussche, Julien VovelleAbstract:Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an Invariant Measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the Invariant Measure. Also, since this Invariant Measure is supported by \(L^p\) for some \(p\) small, we are led to generalize to the stochastic case the theory of \(L^1\) solutions developed by Chen and Perthame (Ann Inst H Poincare Anal Non Lineaire 20(4):645–668, 2003).
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Existence of the Fomin derivative of the Invariant Measure of a stochastic reaction--diffusion equation
2014Co-Authors: Giuseppe Da Prato, Arnaud DebusscheAbstract:We consider a reaction--diffusion equation perturbed by noise (not necessarily white). We prove existence of the Fomin derivative of the corresponding transition semigroup $P_t$. The main tool is a new estimate for $P_tD\varphi$ in terms of $\|\varphi\|_{L^2(H,\nu)}$, where $\nu$ is the Invariant Measure of $P_t$.
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Invariant Measure of scalar first order conservation laws with stochastic forcing
arXiv: Analysis of PDEs, 2013Co-Authors: Arnaud Debussche, Julien VovelleAbstract:Under an hypothesis of non-degeneracy of the flux, we study the long-time behaviour of periodic scalar first-order conservation laws with stochastic forcing in any space dimension. For sub-cubic fluxes, we show the existence of an Invariant Measure. Moreover for sub-quadratic fluxes we show uniqueness and ergodicity of the Invariant Measure. Also, since this Invariant Measure is supported by Lp for some p small, we are led to generalize to the stochastic case the theory of L1 solutions developed by Chen and Perthame in 2003.
Zdzislaw Brzeźniak - One of the best experts on this subject based on the ideXlab platform.
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Invariant Measure for the stochastic navier stokes equations in unbounded 2d domains
Annals of Probability, 2017Co-Authors: Zdzislaw Brzeźniak, Elzbieta Motyl, Martin OndrejatAbstract:Building upon a recent work by two of the authors and J. Seidler on bwbw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an Invariant Measure to stochastic 2-D Navier–Stokes (with multiplicative noise) equations in unbounded domains. This answers an open question left after the first author and Y. Li proved a corresponding result in the case of an additive noise.
Richard W. Martin - One of the best experts on this subject based on the ideXlab platform.
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Beyond Correlation: A Path‐Invariant Measure for Seismogram Similarity
Seismological Research Letters, 2019Co-Authors: Joshua Dickey, Brett J. Borghetti, William N. Junek, Richard W. MartinAbstract:Abstract Similarity search is a popular technique for seismic signal processing, with template matching, matched filters, and subspace detectors being utilized for a wide variety of tasks, including both signal detection and source discrimination. Traditionally, these techniques rely on the cross‐correlation function as the basis for measuring similarity. Unfortunately, seismogram correlation is dominated by path effects, essentially requiring a distinct waveform template along each path of interest. To address this limitation, we propose a novel Measure of seismogram similarity that is explicitly Invariant to path. Using Earthscope’s USArray experiment, a path‐rich dataset of 207,291 regional seismograms across 8452 unique events is constructed, and then employed via the batch‐hard triplet loss function, to train a deep convolutional neural network that maps raw seismograms to a low‐dimensional embedding space, where nearness on the space corresponds to nearness of source function, regardless of path or recording instrumentation. This path‐agnostic embedding space forms a new representation for seismograms, characterized by robust, source‐specific features, which we show to be useful for performing both pairwise event association as well as template‐based source discrimination with a single template.
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beyond correlation a path Invariant Measure for seismogram similarity
arXiv: Geophysics, 2019Co-Authors: Joshua Dickey, Brett J. Borghetti, William N. Junek, Richard W. MartinAbstract:Similarity search is a popular technique for seismic signal processing, with template matching, matched filters and subspace detectors being utilized for a wide variety of tasks, including both signal detection and source discrimination. Traditionally, these techniques rely on the cross-correlation function as the basis for measuring similarity. Unfortunately, seismogram correlation is dominated by path effects, essentially requiring a distinct waveform template along each path of interest. To address this limitation, we propose a novel Measure of seismogram similarity that is explicitly Invariant to path. Using Earthscope's USArray experiment, a path-rich dataset of 207,291 regional seismograms across 8,452 unique events is constructed, and then employed via the batch-hard triplet loss function, to train a deep convolutional neural network which maps raw seismograms to a low dimensional embedding space, where nearness on the space corresponds to nearness of source function, regardless of path or recording instrumentation. This path-agnostic embedding space forms a new representation for seismograms, characterized by robust, source-specific features, which we show to be useful for performing both pairwise event association as well as template-based source discrimination with a single template.
Elzbieta Motyl - One of the best experts on this subject based on the ideXlab platform.
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Invariant Measure for the stochastic navier stokes equations in unbounded 2d domains
Annals of Probability, 2017Co-Authors: Zdzislaw Brzeźniak, Elzbieta Motyl, Martin OndrejatAbstract:Building upon a recent work by two of the authors and J. Seidler on bwbw-Feller property for stochastic nonlinear beam and wave equations, we prove the existence of an Invariant Measure to stochastic 2-D Navier–Stokes (with multiplicative noise) equations in unbounded domains. This answers an open question left after the first author and Y. Li proved a corresponding result in the case of an additive noise.
