The 30th Conference on Stochastic Processes and their Applications (SPA'05) will be held June 26 - July 1, 2005 on the campus of the University of California, at Santa Barbara. Topics to be covered by SPA'05 will include stochastic partial differential equations, random walks on trees, large deviations, mathematical physics, percolation, phase transitions, turbulence, hydrodynamic limits, statistical physics, self-avoiding random walks, random media, spectral theory, random matrices, stochastic networks, queues, simulations, stochastic algorithms, mathematical finance, computational biology, biostatistics, and medical imaging. The conference structure consists of invited talks to be given during the mornings and contributed talks in parallell sessions in the afternoons, as well as opportunities for graduate students, young scientists and senior researchers to mix and learn from each other. Invited speakers are from different parts of the world. Abstracts of the talks will be published on the conference web site.