%0 Book Section %1 py99arc %A Pitman, J. %A Yor, M. %B A Festschrift for Herman Rubin %C Beachwood, OH %D 2004 %E Dasgupta, Anirban %I Institute of Mathematical Statistics %K Dept_Mathematics_Berkeley Dept_Statistics_Berkeley arcsine_law ergodic_theory rational_map myown %P 126--137 %T Some properties of the arc-sine law related to its invariance under a family of rational maps %U http://stat.berkeley.edu/users/pitman/558.pdf %V 45 %X This paper shows how the invariance of the arc sine distribution on $(0,1)$ under a family of rational maps is related on the one hand to various integral identities with probabilistic interpretations involving random variables derived from Brownian motion with arc sine, Gaussian, Cauchy and other distributions, and on the other hand to results in the analytic theory of iterated rational maps.

@incollection{py99arc, abstract = {This paper shows how the invariance of the arc sine distribution on $(0,1)$ under a family of rational maps is related on the one hand to various integral identities with probabilistic interpretations involving random variables derived from Brownian motion with arc sine, Gaussian, Cauchy and other distributions, and on the other hand to results in the analytic theory of iterated rational maps. }, added-at = {2008-01-20T02:39:38.000+0100}, address = {Beachwood, OH}, author = {Pitman, J. and Yor, M.}, bibnumber = {100}, biburl = {https://www.bibsonomy.org/bibtex/24ea6cd405fc562f39a90ea3e1d865379/pitman}, booktitle = {A Festschrift for Herman Rubin}, editor = {Dasgupta, Anirban}, id_ucb-stat = {558}, interhash = {d1c2e82c4fe1c6fda6c9fa7d81ff40cb}, intrahash = {4ea6cd405fc562f39a90ea3e1d865379}, keywords = {Dept_Mathematics_Berkeley Dept_Statistics_Berkeley arcsine_law ergodic_theory rational_map myown}, mrclass = {37F10 (30D05 37A25 60J65)}, mrnumber = {MR2126891 (2005k:37098)}, mrreviewer = {Nathaniel F. G. Martin}, pages = {126--137}, publisher = {Institute of Mathematical Statistics}, series = {IMS Lecture Notes Monogr. Ser.}, timestamp = {2010-10-30T22:51:58.000+0200}, title = {Some properties of the arc-sine law related to its invariance under a family of rational maps}, url = {http://stat.berkeley.edu/users/pitman/558.pdf}, volume = 45, xinstitution = {Dept. Statistics, U.C. Berkeley}, xnumber = {558}, year = 2004 }