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Probability and Real Trees
Steven N. Evans Probability and Real Trees Ecole d’Et´ede Probabilit´es de Saint-Flour XXXV–2005 Editor: J. Picard December 7, 2006 Springer Foreword The Saint-Flour Probability Summer School was founded in 1971. It is sup- ported by CNRS, the “Minist`ere de la Recherche”, and the “Universit´eBlaise Pascal”. Three series of lectures were given at the 35th School (July 6–23, 2005) by the Professors Doney, Evans and Villani. These courses will be published sep- arately, and this volume contains the course of Professor Evans. We cordially thank the author for the stimulating lectures he gave at the school, and for the redaction of these notes. 53 participants have attended this school. 36 of them have given a short lecture. The lists of participants and of short lectures are enclosed at the end of the volume. Here are the references of Springer volumes which have been published prior to this one. All numbers refer to the Lecture Notes in Mathematics series, except S-50 which refers to volume 50 of the Lecture Notes in Statistics series. 1971: vol 307 1980: vol 929 1990: vol 1527 1997: vol 1717 1973: vol 390 1981: vol 976 1991: vol 1541 1998: vol 1738 1974: vol 480 1982: vol 1097 1992: vol 1581 1999: vol 1781 1975: vol 539 1983: vol 1117 1993: vol 1608 2000: vol 1816 1976: vol 598 1984: vol 1180 1994: vol 1648 2001: vol 1837 & 1851 1977: vol 678 1985/86/87: vol 1362 & S-50 2002: vol 1840 & 1875 1978: vol 774 1988: vol 1427 1995: vol 1690 2003: vol 1869 1979: vol 876 1989: vol 1464 1996: vol 1665 2004: vol 1878 & 1879 Further details can be found on the summer school web site http://math.univ-bpclermont.fr/stflour/ Jean Picard Clermont-Ferrand, December 2006 For Ailan Hywel, Ciaran Leuel and Huw Rhys Preface These are notes from a series of ten lectures given at the Saint–Flour Proba- bility Summer School, July 6 – July 23, 2005. -
Priscilla Greenwood: Queen of Probability
Priscilla Greenwood: Queen of Probability I.V. Evstigneev and N.H. Bingham Abstract: This article contains the introduction to the special volume of Stochastics dedicated to Priscilla Greenwood, her CV and her list of publica- tions. This Festschrift celebrates Priscilla Greenwood, a remarkable mathematician, a bright personality and a valued friend and co-author for most of the contributors to the volume. For all of us, she has always been Cindy – Cindy Greenwood, the Queen of Probability. We are happy to mark her outstanding achievements with this Festschrift. This volume contains papers on Probability, Statistics and their appli- cations. But these subjects do not cover all Cindy’s areas of interest and those fields where she left her trace. Her scientific biography, which is sketched below, is unique and remarkable, and it reflects Cindy’s beautiful mind and her true love of science. Cindy Greenwood (C.G.) got into probability from operations research. She was a research assistant in OR at MIT as a graduate student. Feeling the need for stochastics in order to make any real progress, she took a first (and only) stochastic processes course there in 1960 with Henry P. McKean who lectured on the book he was writing with Itˆo. Also in that class were young Ramesh Gangolli, Don Dawson, Bert Fristedt, and Ron Getoor. After that year, C.G. moved to U. Wisconsin, Madison and finished a PhD in ’63 with Josh Chover. The thesis was on a new method of prediction to replace the Wiener-Hopf method when data is on a compact interval. -
Notices of the American Mathematical Society
Calendar of AMS Meetings and Conferences This calendar lists all meetings and conferences approved prior to the date this issue insofar as is possible. Instructions for submission of abstracts can be found in the went to press. The summer and annual meetings are joint meetings with the Mathe January 1993 issue of the Notices on page 46. Abstracts of papers to be presented at matical Association of America. the meeting must be received at the headquarters of the Society in Providence, Rhode Abstracts of papers presented at a meeting of the Society are published in the Island. on or before the deadline given below for the meeting. Note that the deadline for journal Abstracts of papers presented to the American Mathematical Society in the abstracts for consideration for presentation at special sessions is usually three weeks issue corresponding to that of the Notices which contains the program of the meeting, earlier than that specified below. Meetings Abstract Program Meeting# Date Place Deadline Issue 893 June 16-18, 1994 Eugene, Oregon Expired May-June 894 August 15-17, 1994 (96th Summer Meeting) Minneapolis, Minnesota May 17 July-August 895 * October 28-29, 1994 Stillwater, Oklahoma August 3 October 896 * November 11-13, 1994 Richmond, Virginia August 3 October 897 January 4-7, 1995 (101st Annual Meeting) San· Francisco, California OctoberS December 898 March 4-5, 1995 Hartford, Connecticut 899 March 17-18, 1995 Orlando, Florida 900 March 24-25, 1995 Chicago, Illinois August 6-8, 1995 (97th Summer Meeting) Burlington, Vermont October -
Lecture Notes in Mathematics 1897
Lecture Notes in Mathematics 1897 Editors: J.-M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris Subseries: Ecole d’Eté de Probabilités de Saint-Flour Ronald A. Doney Fluctuation Theory for Lévy Processes Ecole d’Eté de Probabilités de Saint-Flour XXXV - 2005 Editor: Jean Picard ABC Author Editor Ronald A. Doney Jean Picard School of Mathematics Laboratoire de Mathématiques Appliquées University of Manchester UMR CNRS 6620 PO Box 88, Sackville Street Université Blaise Pascal (Clermont-Ferrand) Manchester M60 1QD 63177 Aubière Cedex United Kingdom France e-mail: [email protected] e-mail: [email protected] Cover: Blaise Pascal (1623-1662) Library of Congress Control Number: 2007921692 Mathematics Subject Classification (2000): 60G51, 60G10, 60G17, 60J55, 60J75 ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 ISSN Ecole d’Eté de Probabilités de St. Flour, print edition: 0721-5363 ISBN-10 3-540-48510-4 Springer Berlin Heidelberg New York ISBN-13 978-3-540-48510-0 Springer Berlin Heidelberg New York DOI 10.1007/978-3-540-48511-7 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. -
A Summary of Dirichlet Form Theory
A Summary of Dirichlet Form Theory Our treatment in this appendix follows that of the standard reference [72] – see also, [106, 3]. A.1 Non-Negative Definite Symmetric Bilinear Forms Let H be a real Hilbert space with inner product p¨, ¨q. We say E is a non- negative definite symmetric bilinear form on H with domain DpEq if •DpEq is a dense linear subspace of H, •E : DpEq ˆ DpEq Ñ R, •Epu, vq “ Epv, uq for u, v P DpEq, •Epau ` bv, wq “ aEpu, wq ` bEpv, wq for u, v, w P DpEq and a, b P R, •Epu, uq ě 0 for u P DpEq. Given a non-negative definite symmetric bilinear form E on H and α ą 0, define another non-negative definite symmetric bilinear form Eα on H with domain DpEαq :“ DpEq by Eαpu, vq :“ Epu, vq ` αpu, vq, u, v P DpEq. Note that the space DpEq is a pre-Hilbert space with inner product Eα, and Eα and Eβ determine equivalent metrics on DpEq for different α, β ą 0. If DpEq is complete with respect to this metric, then E is said to be closed. In this case, DpEq is then a real Hilbert space with inner product Eα for each α ą 0. A.2 Dirichlet Forms Now consider a σ-finite measure space pX, B, mq and take H to be the Hilbert space L2pX, mq with the usual inner product 164 A Summary of Dirichlet Form Theory pu, vq :“ upxqvpxq mpdxq, u, v P L2pX, mq. żX Call a non-negative definite symmetric bilinear form E on L2pX, mq Markovian if for each ε ą 0, there exists a real function φε : R Ñ R, such that φεptq “ t, t P r0, 1s, ´ ε ď φεptq ď 1 ` ε, t P R, 0 ď φεptq ´ φεpsq ď t ´ s, ´8 ă s ă t ă 8, and when u belongs to DpEq, φε ˝ u also belongs to DpEq with Epφε ˝ u, φε ˝ uq ď Epu, uq. -
Abstracts of the 9-Th International Workshop on Applied Probability
Abstracts of the 9-th International Workshop on Applied Probability 18-21 June 2018, Budapest, Hungary Edited by László Márkus and Vilmos Prokaj The organisation of the International Workshop on Applied Probability is initiated and su- pervised by the IWAP International Board. The IWAP International Board Joseph Glaz (chair), University of Connecticut, USA Jürg Hüsler, University of Bern, Switzerland Nikolaos Limnios, Technical University of Compiegne, France Markos Koutras, University of Piraeus, Greece José Luis Palacios, University of New Mexico, USA; University Simón Bolívar, Venezuela The IWAP International Board appointed the committees below. The Scientific Programme Committee: Co-chairs: Joseph Glaz, University of Connecticut, USA László Márkus, Eötvös Loránd University, Hungary Jogesh Babu, Pennsylvania State University, USA Narayanaswamy Balakrishnan, McMaster University, Canada Viktor Beneš, Charles University, Prague, Czech Republic Alexander Bulinski, Lomonosov Moscow State University, Russia Krzysztof Dębicki, University Wroclaw, Poland Serkan Eryilmaz, Atilim University, Ankara, Turkey Enkelejd Hashorva, HEC Lausanne, Switzerland Remco van der Hofstad, Technische Universiteit Eindhoven, The Netherlands Blanka Horváth, Imperial College, London, UK Ron Kenett, Samuel Neaman Institute, Technion, Israel and KPA Ltd., Raanana, Israel Claude Lefevre, University Libre de Bruxelles, Belgium Haijun Li, Washington State University, USA Wendy Lou, University of Toronto, Canada Nitis Mukhopadhyay, University of Connecticut, USA Mark