Table Of Content

ILLINOIS JOURNAL OF MATHEMATICS Contents of Volume 50 (2006) Rodrigo Banuelos, Pedro J. Méndez-Hernandez, Hot-spots for conditioned Brownian motion Martin T. Barlow, Takashi Kumagai, Random walk on the incipient infinite cluster on trees Federico Bassetti, Persi Diaconis, Examples comparing importance sampling and the Metropolis algorithm Robert O. Bauer, Roland M. Friedrich, Diffusing polygons and SLE(k,p ) Istvan Berkes, Walter Philipp, Robert F. Tichy, Empirical processes in probabilistic number theory: the LIL for the discrepancy of (n;,w) mod 1 Jean Bertoin, Jean-Francois Le Gall, Stochastic flows associated to coalescent processes III: Limit theorems Jean Bourgain, Nonlinear Schrodinger equation with a random potential Krzysztof Burdzy, Zhen-Qing Chen, Peter Jones, Synchronous couplings of reflected Brownian motions in smooth domains Donald Burkholder, Joseph Leo Doob (1910-2004) Zhen-Qing Chen, Masatoshi Fukushima, Jiangang Ying, Entrance law, exit system and Lévy system of tine changed processes Zhen-Qing Chen, Krzysztof Burdzy, Peter Jones, Synchronous couplings of reflected Brownian motions in smooth domains Burgess Davis, Jiyeon Suh, On Burkholder’s supermartingales D.A. Dawson, E.A. Perkins, On the uniqueness problem for catalytic branching networks and other singular diffusions Persi Diaconis, Federico Bassetti, Examples comparing importance sampling and the Metropolis algorithm E.B. Dynkin, A note on X-harmonic functions P.J. Fitzsimmons, R.K. Getoor, Excursion theory revisited Hans Foéllmer, Anne Gundel, Robust projections in the class of martingale measures Roland M. Friedrich, Robert O. Bauer, Diffusing polygons and SLE(k,p ) Masatoshi Fukushima, Zhen-Qing Chen, Jiangang Ying, Entrance law, exit system and Lévy system of time changed processes R.K. Getoor, P.J. Fitzsimmons, Excursion theory revisited Anne Gundel, Hans Féllmer, Robust projections in the class of martingale measures Istvan Gyoéngy, Nicolai Krylov, Expansion of solutions of parameterized equations and acceleration of numerical methods Peter Jones, Krzysztof Burdzy, Zhen-Qing Chen, Synchronous couplings of reflected Brownian motions in smooth domains Yuji Kasahara, Shinzo Watanabe, Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes Robert Kaufman, Mixing and descriptive set theory Harry Kesten, Vladas Sidoravicius, A phase transition in a model for the spread of an infection Panki Kim, Renming Song, Two-sided estimates on the density of Brownian Motion with singular drift F.B. Knight, J.L. Steichen, The probability of escaping interference Nicolai Krylov, Istvan Gyoéngy, Expansion of solutions of parameterized equations and acceleration of numerical methods Takashi Kumagai, Martin T. Barlow, Random walk on the incipient infinite cluster on trees Gregory F. Lawler, The Laplacian-b random walk and the Schramm-Loewner Evolution Jean-Francois Le Gall, Jean Bertoin, Stochastic flows associated to coalescent processes III: Limit theorems Peter Loeb, Yeneng Sun, Purification of measure-valued maps Terry J. Lyons, Nadia Sidorova, On the radius of convergence of the logarithmic signature Pedro J. Méndez-Hernandez, Rodrigo Banuelos, Hot~spots for conditioned Brownian motion Michel Emery, Chaotic representation property of certain Azéma martingales Ashkan Nikeghbali, Marc Yor, Doob’s maximal identity, multiplicative decompositions and enlargements of filtrations E.A. Perkins, D.A. Dawson, On the uniqueness problem for catalytic branching networks and other singular diffusions Walter Philipp, Istvan Berkes, Robert F. Tichy, Empirical processes in probabilistic number theory: the LIL for the discrepancy of (n;w) mod 1 Dmitry Rokhlin, Walter Schachermayer, A note on lower bounds of martingale measure densities Ken-iti Sato, Additive processes and stochastic integrals Walter Schachermayer, Dmitry Rokhlin, A note on lower bounds of martingale measure densities Vladas Sidoravicius, Harry Kesten, A phase transition in a model for the spread of an infection Nadia Sidorova, Terry J. Lyons, On the radius of convergence of the logarithmic signature Renming Song, Panki Kim, Two-sided estimates on the density of Brownian Motion with singular drift Richard B. Sowers, Random perturbations of two-dimensional pseudoperiodic flows J.L. Steichen, F.B. Knight, The probability of escaping interference Daniel W. Stroock, David Williams, Further study of a simple PDE Jiyeon Suh, Burgess Davis, On Burkholder’s supermartingales Yeneng Sun, Peter Loeb, Purification of measure-valued maps Robert F. Tichy, Istvan Berkes, Walter Philipp, Empirical processes in probabilistic number theory: the LIL for the discrepancy of (n,w) mod 1 107 John B. Walsh, On numerical solutions of the stochastic wave equation 991 Shinzo Watanabe, Yuji Kasahara, Brownian representation of a class of Lévy processes and its application to occupation times of diffusion processes 515 David Williams, Daniel W. Stroock, Further study of a simple PDE 961 Jang-Mei Wu, Doob’s contribution to function theory 1019 Jiangang Ying, Zhen-Qing Chen, Masatoshi Fukushima, Entrance law, exit system and Lévy system of time changed processes 269 Marc Yor, Ashkan Nikeghbali, Doob’s maximal identity, multiplicative decompositions and enlargements of filtrations 791