This proposal requests travel support for U.S. participants attending the 31st Conference on Stochastic Processes and their Applications, an international meeting to be held July 17-21, 2006 in Paris, France. The conference on Stochastic Processes and their Applications have become the principal annual international forum for researchers studying applied and theoretical problems in stochastic processes. These conferences provide a balanced and broad overview of current research in probability and areas of application and bring together distinguished scholars from all over the world.