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Books on the topic 'Stochastic Fokker-Planck'

Author: Grafiati

Published: 14 December 2024

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1

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

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2

Grasman, Johan. Asymptotic methods for the Fokker-Planck equation and the exit problem in applications. Berlin: Springer, 1999.

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3

Chirikjian, Gregory S. Stochastic models, information theory, and lie groups. Boston: Birkhäuser, 2009.

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4

Fokker-Planck-Kolmogorov equations. Providence, Rhode Island: American Mathematical Society, 2015.

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5

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

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6

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

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7

Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer, 2014.

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8

Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer, 2016.

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9

Pavliotis, Grigorios A. Stochastic Processes and Applications: Diffusion Processes, the Fokker-Planck and Langevin Equations. Springer London, Limited, 2014.

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10

McClintock, P. V. E., and Frank Moss. Noise in Nonlinear Dynamical Systems Vol. 1: Theory of Continuous Fokker-Planck Systems. Cambridge University Press, 2007.

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11

McClintock, P. V. E., and Frank Moss. Noise in Nonlinear Dynamical Systems: Volume 1, Theory of Continuous Fokker-Planck Systems. Cambridge University Press, 2012.

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12

(Editor), Peter H. Baxendale, and Sergey V. Lototsky (Editor), eds. Stochastic Differential Equations: Theory and Applications, a Volume in Honor of Professor Boris L Rozovskii (Interdisciplinary Mathematical Sciences) (Interdisciplinary Mathematical Sciences). World Scientific Publishing Company, 2007.

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13

Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions. World Scientific Publishing Co Pte Ltd, 1994.

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14

Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions. World Scientific Publishing Co Pte Ltd, 1994.

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15

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

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16

Succi, Sauro. Stochastic Particle Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780199592357.003.0009.

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Dense fluids and liquids molecules are in constant interaction; hence, they do not fit into the Boltzmann’s picture of a clearcut separation between free-streaming and collisional interactions. Since the interactions are soft and do not involve large scattering angles, an effective way of describing dense fluids is to formulate stochastic models of particle motion, as pioneered by Einstein’s theory of Brownian motion and later extended by Paul Langevin. Besides its practical value for the study of the kinetic theory of dense fluids, Brownian motion bears a central place in the historical development of kinetic theory. Among others, it provided conclusive evidence in favor of the atomistic theory of matter. This chapter introduces the basic notions of stochastic dynamics and its connection with other important kinetic equations, primarily the Fokker–Planck equation, which bear a complementary role to the Boltzmann equation in the kinetic theory of dense fluids.

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17

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

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18

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

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19

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

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20

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

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21

Modeling with Itô Stochastic Differential Equations. Springer, 2007.

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22

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

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23

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

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24

Henriksen, Niels Engholm, and Flemming Yssing Hansen. Introduction to Condensed-Phase Dynamics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198805014.003.0009.

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This chapter discusses chemical reactions in solution; first, how solvents modify the potential energy surface of the reacting molecules and second, the role of diffusion. As a first approximation, solvent effects are described by models where the solvent is represented by a dielectric continuum, focusing on the Onsager reaction-field model for solvation of polar molecules. The reactants of bimolecular reactions are brought into contact by diffusion, and the interplay between diffusion and chemical reaction that determines the overall reaction rate is described. The solution to Fick’s second law of diffusion, including a term describing bimolecular reaction, is discussed. The limits of diffusion control and activation control, respectively, are identified. It concludes with a stochastic description of diffusion and chemical reaction based on the Fokker–Planck equation, which includes the diffusion of particles interacting via a potential U(r).

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25

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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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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26

Stochastic Models, Information Theory, and Lie Groups, Volume 1 Vol. 1: Classical Results and Geometric Methods. Birkhauser Verlag, 2009.

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