The equation of Camassa and Holm [2]2 is an approximate description of long waves in shallow water.
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Preface 1. Preliminaries 2. Bernoulli trials 3. The standard random walk 4. The standard random walk in higher dimensions 5. LLN, CLT, iterated log, and arcsine in general 6. Brownian motion 7. Markov chains 8. The ergodic theorem 9. Communication over a noisy channel 10. Equilibrium statistical mechanics 11. Statistical mechanics out of equilibrium 12. Random matrices Bibliography Index.
The article provides with a down to earth exposition of the Fredholm theory with applications to Brownian motion and KdV equation.
. This paper recollects the author’s encounter with Itô in Princeton 1954 and their collaboration on diffusion process and their sample path.
Communications on Pure and Applied MathematicsVolume 57, Issue 3 p. 416-418 Breakdown of the Camassa-Holm equation Henry P. McKean, Henry P. McKean mckean@cims.nyu.edu Courant Institute, 251 Mercer Street New York, NY 10012-1185Search for more papers by this author Henry P. McKean, Henry P. McKean mckean@cims.nyu.edu Courant Institute, 251 Mercer Street New York, NY 10012-1185Search for more papers by this author First published: 17 December 2003 https://doi.org/10.1002/cpa.20003Citations: 70AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article.Citing Literature Volume57, Issue3March 2004Pages 416-418 RelatedInformation
Communications on Pure and Applied MathematicsVolume 56, Issue 7 p. 998-1015 The Liouville correspondence between the Korteweg—de Vries and the Camassa-Holm hierarchies Henry P. McKean, Henry P. McKean mckean@cims.nyu.edu Courant Institute, 251 Mercer Street, New York, NY 10012-1185Search for more papers by this author Henry P. McKean, Henry P. McKean mckean@cims.nyu.edu Courant Institute, 251 Mercer Street, New York, NY 10012-1185Search for more papers by this author First published: 23 April 2003 https://doi.org/10.1002/cpa.10083Citations: 31AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume56, Issue7Special Issue: First of Two Special Issues Dedicated to the Memory of Jürgen K. MoserJuly 2003Pages 998-1015 RelatedInformation
Communications on Pure and Applied MathematicsVolume 54, Issue 10 p. 1271-1288 Addition for the acoustic equation Henry P. McKean, Henry P. McKean [email protected] Courant Institute, 251 Mercer Street, New York, NY 10012-1185Search for more papers by this author Henry P. McKean, Henry P. McKean [email protected] Courant Institute, 251 Mercer Street, New York, NY 10012-1185Search for more papers by this author First published: 31 July 2001 https://doi.org/10.1002/cpa.10003Citations: 5AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Citing Literature Volume54, Issue10October 2001Pages 1271-1288 RelatedInformation