This IMA Volume in Mathematics and its Applications PROBABILITY AND PARTIAL DIFFERENTIAL EQUATIONS IN MODERN APPLIED MATHEMATICS contains a selection of articles presented at 2003 IMA Summer Program with the same title. We would like to thank Jinqiao Duan (Department of Applied Mathe­ matics, Illinois Institute of Technology) and Edward C. Waymire (Depart­ ment of Mathematics, Oregon State University) for their excellent work as organizers of the two-weeksummer workshop and for editing the volume. We also take this opportunity to thank the National Science Founda­ tion for their support of the IMA. Series Editors Douglas N. Arnold, Director of the IMA Fadil Santosa, Deputy Director of the IMA PREFACE The IMA Summer Program on Probability and Partial Differential Equations in Modern Applied Mathematics took place July 21-August 1, 2003, a fitting segue to the IMA annual program on Probability and Statis­ tics in Complex Systems: Genomics, Networks, and Financial Engineering which was to begin September, 2003. In addition to the outstanding re­ sources and staff at IMA, the summer program was developed with the assistance of the followingmembers of the organizing committee: Rabi N. Bhattacharya, Larry Chen, Jinqiao Duan, Ronald B. Guenther, Peter E. Kloeden, Salah Mohammed, Sri Namachchivaya, Mina Ossiander, Bjorn Schmalfuss, Enrique Thomann, and Ed Waymire.