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Relevant bibliographies by topics / Measure-valued equations

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Academic literature on the topic 'Measure-valued equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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Journal articles on the topic "Measure-valued equations"

1

Artstein, Zvi. "On singularly perturbed ordinary differential equations with measure-valued limits." Mathematica Bohemica 127, no. 2 (2002): 139–52. http://dx.doi.org/10.21136/mb.2002.134168.

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S. Ackleh, Azmy, Nicolas Saintier, and Jakub Skrzeczkowski. "Sensitivity equations for measure-valued solutions to transport equations." Mathematical Biosciences and Engineering 17, no. 1 (2020): 514–37. http://dx.doi.org/10.3934/mbe.2020028.

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Dawson, Donald A., and Zenghu Li. "Stochastic equations, flows and measure-valued processes." Annals of Probability 40, no. 2 (March 2012): 813–57. http://dx.doi.org/10.1214/10-aop629.

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Wang, Feng-Yu. "Itô type measure-valued stochastic differential equations." Journal of Mathematical Analysis and Applications 329, no. 2 (May 2007): 1102–17. http://dx.doi.org/10.1016/j.jmaa.2006.07.029.

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Feshchenko, O. Yu. "On Measure-Valued Processes Generated by Differential Equations." Ukrainian Mathematical Journal 55, no. 4 (April 2003): 632–42. http://dx.doi.org/10.1023/b:ukma.0000010162.97417.76.

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Tesei, Alberto. "Radon measure-valued solutions of quasilinear parabolic equations." Rendiconti Lincei - Matematica e Applicazioni 32, no. 2 (July 14, 2021): 213–31. http://dx.doi.org/10.4171/rlm/934.

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Lanthaler, Samuel, and Siddhartha Mishra. "Computation of measure-valued solutions for the incompressible Euler equations." Mathematical Models and Methods in Applied Sciences 25, no. 11 (July 10, 2015): 2043–88. http://dx.doi.org/10.1142/s0218202515500529.

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We combine the spectral (viscosity) method and ensemble averaging to propose an algorithm that computes admissible measure-valued solutions of the incompressible Euler equations. The resulting approximate young measures are proved to converge (with increasing numerical resolution) to a measure-valued solution. We present numerical experiments demonstrating the robustness and efficiency of the proposed algorithm, as well as the appropriateness of measure-valued solutions as a solution framework for the Euler equations. Furthermore, we report an extensive computational study of the two-dimensional vortex sheet, which indicates that the computed measure-valued solution is non-atomic and implies possible non-uniqueness of weak solutions constructed by Delort.

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Rémillard, Bruno, and Jean Vaillancourt. "On signed measure valued solutions of stochastic evolution equations." Stochastic Processes and their Applications 124, no. 1 (January 2014): 101–22. http://dx.doi.org/10.1016/j.spa.2013.07.003.

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Méléard, Sylvie, and Sylvie Roelly. "Discontinuous Measure-Valued Branching Processes and Generalized Stochastic Equations." Mathematische Nachrichten 154, no. 1 (1991): 141–56. http://dx.doi.org/10.1002/mana.19911540112.

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Camilli, Fabio, Raul De Maio, and Andrea Tosin. "Measure-valued solutions to nonlocal transport equations on networks." Journal of Differential Equations 264, no. 12 (June 2018): 7213–41. http://dx.doi.org/10.1016/j.jde.2018.02.015.

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Dissertations / Theses on the topic "Measure-valued equations"

1

Wiedemann, Emil [Verfasser]. "Weak and measure-valued solutions of the incompressible Euler equations / Emil Wiedemann." Bonn : Universitäts- und Landesbibliothek Bonn, 2012. http://d-nb.info/1043911308/34.

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Seadler, Bradley T. "Signed-Measure Valued Stochastic Partial Differential Equations with Applications in 2D Fluid Dynamics." Case Western Reserve University School of Graduate Studies / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=case1333062148.

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Pace, Michele. "Stochastic models and methods for multi-object tracking." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2011. http://tel.archives-ouvertes.fr/tel-00651396.

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La poursuite multi-cibles a pour objet le suivi d'un ensemble de cibles mobiles à partir de données obtenues séquentiellement. Ce problème est particulièrement complexe du fait du nombre inconnu et variable de cibles, de la présence de bruit de mesure, de fausses alarmes, d'incertitude de détection et d'incertitude dans l'association de données. Les filtres PHD (Probability Hypothesis Density) constituent une nouvelle gamme de filtres adaptés à cette problématique. Ces techniques se distinguent des méthodes classiques (MHT, JPDAF, particulaire) par la modélisation de l'ensemble des cibles comme un ensemble fini aléatoire et par l'utilisation des moments de sa densité de probabilité. Dans la première partie, on s'intéresse principalement à la problématique de l'application des filtres PHD pour le filtrage multi-cibles maritime et aérien dans des scénarios réalistes et à l'étude des propriétés numériques de ces algorithmes. Dans la seconde partie, nous nous intéressons à l'étude théorique des processus de branchement liés aux équations du filtrage multi-cibles avec l'analyse des propriétés de stabilité et le comportement en temps long des semi-groupes d'intensités de branchements spatiaux. Ensuite, nous analysons les propriétés de stabilité exponentielle d'une classe d'équations à valeurs mesures que l'on rencontre dans le filtrage non-linéaire multi-cibles. Cette analyse s'applique notamment aux méthodes de type Monte Carlo séquentielles et aux algorithmes particulaires dans le cadre des filtres de Bernoulli et des filtres PHD.

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Carroll, Colin. "Minimizers of the vector-valued coarea formula." Thesis, 2012. http://hdl.handle.net/1911/64635.

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The vector-valued coarea formula provides a relationship between the integral of the Jacobian of a map from high dimensions down to low dimensions with the integral over the measure of the fibers of this map. We explore minimizers of this functional, proving existence using both a variational approach and an approach with currents. Additionally, we consider what properties these minimizers will have and provide examples. Finally, this problem is considered in metric spaces, where a third existence proof is given.

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Books on the topic "Measure-valued equations"

1

Weak and measure-valued solutions to evolutionary PDEs. London: Chapman and Hall, 1996.

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2

Necas, J., J. Malek, M. Rokyta, and M. Ruzicka. Weak and Measure-Valued Solutions to Evolutionary PDEs. Taylor & Francis Group, 2019.

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Necas, J., J. Malek, M. Rokyta, and M. Ruzicka. Weak and Measure-Valued Solutions to Evolutionary PDEs. Taylor & Francis Group, 2019.

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4

Josef, Málek, ed. Weak and measure-valued solutions to evolutionary PDEs. London: Chapman & Hall, 1996.

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5

1937-, Dawson Donald Andrew, and Université de Montréal. Centre de recherches mathématiques., eds. Measure-valued processes, stochastic partial differential equations, and interacting systems. Providence, R.I., USA: American Mathematical Society, 1994.

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Necas, J., J. Malek, M. Rokyta, and M. Ruzicka. Weak and Measure-Valued Solutions to Evolutionary PDEs (Applied Mathematics and Mathematical Computation Series). Chapman & Hall/CRC, 1996.

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Boudou, Alain, and Yves Romain. On Product Measures Associated with Stationary Processes. Edited by Frédéric Ferraty and Yves Romain. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780199568444.013.15.

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This article considers the connections between product measures and stationary processes. It first provides an overview of historical facts and relevant terminology, basic concepts and the mathematical approach. In particular, it discusses random measures, the projection-valued spectral measure (PVSM), convolution products, and the association between shift operators and PVSMs. It then presents the main results and their first potential applications, focusing on stochastic integrals, the image of a random measure under measurable mapping, the existence of a transport-type theorem, and the transpose of a continuous homomorphism between groups. It also describes the PVSM associated with a unitary operator, the convolution product of two PVSMs, the unitary operators generated by a PVSM, extension of the convolution product of two PVSMs, an equation where the unknown quantity is a PVSM, and the convolution product of two random measures. The article concludes with an analysis of mathematical developments related to the previous results.

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Book chapters on the topic "Measure-valued equations"

1

Zhao, Xuelei. "On the Interacting Measure-Valued Branching Processes." In Stochastic Differential and Difference Equations, 345–53. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-1980-4_28.

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Málek, J., J. Nečas, M. Rokyta, and M. Růžička. "Measure-valued solutions and nonlinear hyperbolic equations." In Weak and Measure-valued Solutions to Evolutionary PDEs, 169–91. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4899-6824-1_4.

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Brigo, Damiano, and Giovanni Pistone. "Dimensionality Reduction for Measure Valued Evolution Equations in Statistical Manifolds." In Computational Information Geometry, 217–65. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-47058-0_10.

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4

el Karoui, Nicole. "Non-linear evolution equations and functionnals of measure-valued branching processes." In Lecture Notes in Control and Information Sciences, 25–34. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0005056.

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5

Slemrod, M. "Measure Valued Solutions to a Backward-Forward Heat Equation: A Conference Report." In The IMA Volumes in Mathematics and Its Applications, 232–42. New York, NY: Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4613-9049-7_17.

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Málek, J., J. Nečas, M. Rokyta, and M. Růžička. "Measure-valued solutions and nonlinear hyperbolic equations." In Weak and Measure-valued Solutions to Evolutionary PDEs, 169–92. Chapman and Hall/CRC, 2019. http://dx.doi.org/10.1201/9780367810771-4.

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7

"Reduced Hausdorff Dimension, Oscillations, and Measure-Valued Solutions of the Euler Equations in Two and Three Dimensions." In Vorticity and Incompressible Flow, 450–97. Cambridge University Press, 2001. http://dx.doi.org/10.1017/cbo9780511613203.013.

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Conference papers on the topic "Measure-valued equations"

1

Chakrabarti, Suryarghya, and Marcelo J. Dapino. "Modeling of a Displacement Amplified Magnetostrictive Actuator for Active Mounts." In ASME 2009 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. ASMEDC, 2009. http://dx.doi.org/10.1115/smasis2009-1411.

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A hydraulically-amplified Terfenol-D actuator is developed to be used as a driver in active engine mounts. A measure of the actuator’s performance is obtained through electromechanical tests in mechanically-blocked and mechanically-free conditions. A nonlinear model for the actuator is presented. The Jiles-Atherton model is coupled with Maxwell’s equations in order to quantify the radial dependence of magnetization and associated dynamic losses. Magnetostriction, which is modeled as a single-valued function of magnetization, provides an input to the mechanical model describing the system vibrations. Friction at the elastomeric seals is modeled using the LuGre friction model for lubricated contacts. Results show that the model is able to accurately describe the dynamic behavior of the actuator up to 400 Hz. An order analysis on the data and modeled responses show that the model is capable of describing the higher harmonic content of the device with sufficient accuracy for control design.

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2

Wang, Yan. "Simulating Drift-Diffusion Processes With Generalized Interval Probability." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70699.

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The Fokker-Planck equation is widely used to describe the time evolution of stochastic systems in drift-diffusion processes. Yet, it does not differentiate two types of uncertainties: aleatory uncertainty that is inherent randomness and epistemic uncertainty due to lack of perfect knowledge. In this paper, a generalized Fokker-Planck equation based on a new generalized interval probability theory is proposed to describe drift-diffusion processes under both uncertainties, where epistemic uncertainty is modeled by the generalized interval while the aleatory one is by the probability measure. A path integral approach is developed to numerically solve the generalized Fokker-Planck equation. The resulted interval-valued probability density functions rigorously bound the real-valued ones computed from the classical path integral method. The new approach is demonstrated by numerical examples.

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3

Wang, Yan. "Solving Interval Master Equation in Simulation of Jump Processes Under Uncertainties." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12740.

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Two types of uncertainty are generally recognized in modeling and simulation, including variability caused by inherent randomness and incertitude due to the lack of perfect knowledge. Generalized interval probability is able to model both uncertainty components simultaneously, where epistemic uncertainty is quantified by the generalized interval in addition to the probabilistic measure. With the conditioning, independence, and Markovian property uniquely defined, the calculus structures in generalized interval probability resembles those in the classical probability theory. An imprecise Markov chain model is proposed with the ease of computation. A Krylov subspace projection method is developed to solve the interval master equation to simulate jump processes with finite state transitions under uncertainties. The state transitions with interval-valued probabilities can be simulated, which provides the lower and upper bound information of evolving distributions as an alternative to the traditional sensitivity analysis.

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