Fields Institute Communications Volume 00, 0000 OurjointworkwithMikl´osCs¨org˝o Endre Cs´ aki A. R´ enyi Institute of Mathematics Hungarian Academy of Sciences P.O.B. 127 H-1364 Budapest Hungary csaki@renyi.hu Ant´ onia F¨ oldes Department of Mathematics City University of New York 2800 Victory Blvd. Staten Island, New York 10314 U.S.A. afoldes@gc.cuny.edu Zhan Shi Laboratoire de Probabilit´ es UMR 7599 Universit´ e Paris VI 4 Place Jussieu F-75252 Paris Cedex 05 France zhan@proba.jussieu.fr Dedicated to Mikl´os Cs¨org˝o on the occasion of his 70-th birthday Abstract. Topics in our joint work of twenty years are discussed. To name a few: asymptotic independence, strong approximation of additive functionals, iterated processes, path properties of the Cauchy principal value, Vervaat process. 1. Introduction The work of Mikl´ os Cs¨ org˝ o has a tremendous impact on modern probability and statistics. His books and papers are bibles for the young generation of these 2000 Mathematics Subject Classification. Primary 60J55; Secondary 60F15, 60F17, 60J15. Research of the first author supported by the Hungarian National Foundation for Scientific Research, Grant Nos. T 029621 and T 037886. Research of the second author supported by a PSC CUNY grant, No. 634680032. Cooperation between the authors supported by the joint French-Hungarian Intergovernmental Grant ”Balaton”, No. F-39/2000. c 0000 American Mathematical Society 1