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Books on the topic 'McKean stochastic differential equation'

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Published: 1 June 2024

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1

Peszat, S. Stochastic partial differential equations with Lévy noise: An evolution equation approach. Cambridge: Cambridge University Press, 2007.

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2

Prato, Giuseppe Da. Introduction to stochastic analysis and Malliavin calculus. Pisa, Italy: Edizioni della Normale, 2007.

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3

Tadahisa, Funaki, and Woyczyński W. A. 1943-, eds. Nonlinear stochastic PDE's: Hydrodynamic limit and Burgers' turbulence. New York: Springer, 1996.

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4

Frank, T. D. Nonlinear Fokker-Planck equations: Fundamentals and applications. Berlin: Springer, 2004.

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5

Sowers, R. B. Short-time geometry of random heat kernels. Providence, R.I: American Mathematical Society, 1998.

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6

Sowers, R. B. Short-time geometry of random heat kernels. Providence, R.I: American Mathematical Society, 1998.

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7

Dalang, Robert C. H\older-Sobolev regularity of the solution to the stochastic wave equation in dimension three. Providence, R.I: American Mathematical Society, 2009.

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8

Soize, Christian. The Fokker-Planck equation for stochastic dynamical systems and its explicit steady state solutions. Singapore: World Scientific, 1994.

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9

Lawler, Gregory F. Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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10

Pascal, Auscher, Coulhon T, and Grigoryan A, eds. Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs, April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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11

Frank, Till Daniel. Nonlinear Fokker-Planck equations: Fundamentals and applications. Berlin: Springer, 2005.

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12

I, Bogachev V., N. V. Krylov, Michael Röckner, and Stanislav V. Shaposhnikov. Fokker-Planck-Kolmogorov equations. Providence, Rhode Island: American Mathematical Society, 2015.

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13

Calin, Ovidiu. Heat Kernels for Elliptic and Sub-elliptic Operators: Methods and Techniques. Boston: Springer Science+Business Media, LLC, 2011.

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14

Ammari, Habib. Imaging, multi-scale, and high-contrast partial differential equations: Seoul ICM 2014 Satellite Conference, August 7-9, 2014, Daejeon, Korea. Providence, Rhode Island: American Mathematical Society, 2016.

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15

Allen, E. Modeling with Itô Stochastic Differential Equations. Springer, 2007.

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16

Ohira, Toru. A master equation approach to stochastic neurodynamics. 1993.

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17

Zabczyk, J., and S. Peszat. Stochastic Partial Differential Equations with lévy Noise: An Evolution Equation Approach. Cambridge University Press, 2007.

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18

Zabczyk, J., and S. Peszat. Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach. Cambridge University Press, 2010.

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19

Zabczyk, J., and S. Peszat. Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach. Cambridge University Press, 2012.

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20

Coffey, William T. Langevin Equation: With Applications to Stochastic Problems in Physics, Chemistry and Electrical Engineering. World Scientific Publishing Co Pte Ltd, 2017.

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21

Susnjara, Anna, and Dragan Poljak. Deterministic and Stochastic Modeling in Computational Electromagnetics: Integral and Differential Equation Approaches. Wiley & Sons, Incorporated, John, 2023.

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22

Susnjara, Anna, and Dragan Poljak. Deterministic and Stochastic Modeling in Computational Electromagnetics: Integral and Differential Equation Approaches. Wiley & Sons, Incorporated, John, 2023.

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23

Susnjara, Anna, and Dragan Poljak. Deterministic and Stochastic Modeling in Computational Electromagnetics: Integral and Differential Equation Approaches. Wiley & Sons, Incorporated, John, 2023.

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24

Allen, E. Modeling with Itô Stochastic Differential Equations. Springer London, Limited, 2007.

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25

Zabczyk, J., and S. Peszat. Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach (Encyclopedia of Mathematics and its Applications). Cambridge University Press, 2007.

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26

Kuksin, Sergej B., and Alexandre Boritchev. One-Dimensional Turbulence and the Stochastic Burgers Equation. American Mathematical Society, 2021.

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27

(Editor), Tadahisa Funaki, and Wojbor Woyczynski (Editor), eds. Nonlinear Stochastic PDE's: Hydrodynamic Limit and Burgers' Turbulence (The IMA Volumes in Mathematics and its Applications). Springer, 1995.

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28

Allen, E. Modeling with Itô Stochastic Differential Equations: Theory and Applications). E Allen, 2010.

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29

Heat kernels and analysis on manifolds, graphs, and metric spaces: Lecture notes from a quarter program on heat kernels, random walks, and analysis on manifolds and graphs : April 16-July 13, 2002, Emile Borel Centre of the Henri Poincaré Institute, Paris, France. Providence, R.I: American Mathematical Society, 2003.

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30

(Editor), Pascal Auscher, T. Coulhon (Editor), and A. Grigoryan (Editor), eds. Heat Kernels and Analysis on Manifolds, Graphs, and Metric Spaces: Lecture Notes from a Quarter Program on Heat Kernels, Random Walks, and Analysis on ... Borel Centre of (Contemporary Mathematics). American Mathematical Society, 2004.

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31

Prato, Giuseppe Da. Introduction to Stochastic Analysis and Malliavin Calculus. Scuola Normale Superiore, 2014.

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32

Prato, Giuseppe Da, and Ville Turunen. Introduction to Stochastic Analysis and Malliavin Calculus. Scuola Normale Superiore, 2009.

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33

Prato, Giuseppe Da. Introduction to Stochastic Analysis and Malliavin Calculus. Edizioni della Normale, 2014.

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34

Keener, James P. Biology in Time and Space: A Partial Differential Equation Modeling Approach. American Mathematical Society, 2021.

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35

Krylov, Nicolai V., Michael Rockner, Vladimir I. Bogachev, and Stanislav V. Shaposhnikov. Fokker-Planck-Kolmogorov Equations. American Mathematical Society, 2015.

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36

Eriksson, Olle, Anders Bergman, Lars Bergqvist, and Johan Hellsvik. Atomistic Spin Dynamics. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788669.001.0001.

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Abstract:
The purpose of this book is to provide a theoretical foundation and an understanding of atomistic spin-dynamics, and to give examples of where the atomistic Landau-Lifshitz-Gilbert equation can and should be used. The contents involve a description of density functional theory both from a fundamental viewpoint as well as a practical one, with several examples of how this theory can be used for the evaluation of ground state properties like spin and orbital moments, magnetic form-factors, magnetic anisotropy, Heisenberg exchange parameters, and the Gilbert damping parameter. This book also outlines how interatomic exchange interactions are relevant for the effective field used in the temporal evolution of atomistic spins. The equation of motion for atomistic spin-dynamics is derived starting from the quantum mechanical equation of motion of the spin-operator. It is shown that this lead to the atomistic Landau-Lifshitz-Gilbert equation, provided a Born-Oppenheimer-like approximation is made, where the motion of atomic spins is considered slower than that of the electrons. It is also described how finite temperature effects may enter the theory of atomistic spin-dynamics, via Langevin dynamics. Details of the practical implementation of the resulting stochastic differential equation are provided, and several examples illustrating the accuracy and importance of this method are given. Examples are given of how atomistic spin-dynamics reproduce experimental data of magnon dispersion of bulk and thin-film systems, the damping parameter, the formation of skyrmionic states, all-thermal switching motion, and ultrafast magnetization measurements.
37

Brezin, Edouard, and Sinobu Hikami. Beta ensembles. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.20.

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Abstract:
This article deals with beta ensembles. Classical random matrix ensembles contain a parameter β, taking on the values 1, 2, and 4. This parameter, which relates to the underlying symmetry, appears as a repulsion sβ between neighbouring eigenvalues for small s. β may be regarded as a continuous positive parameter on the basis of different viewpoints of the eigenvalue probability density function for the classical random matrix ensembles - as the Boltzmann factor for a log-gas or the squared ground state wave function of a quantum many-body system. The article first considers log-gas systems before discussing the Fokker-Planck equation and the Calogero-Sutherland system. It then describes the random matrix realization of the β-generalization of the circular ensemble and concludes with an analysis of stochastic differential equations resulting from the case of the bulk scaling limit of the β-generalization of the Gaussian ensemble.
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