SS75 AIMS 2016 Meeting, Orlando, Florida, USA

Title:  Recent trends on PDEs driven by Gaussian processes with applications
Organizer(s):
Name: Affiliation: Country: Email Address:
Hakima Bessaih
University of Wyoming
USA
bessaih@uwyo.edu
Maria J. Garrido-Atienza
University of Seville
Spain
mgarrido@us.es
Introduction:
We are interested in the theory and applications of stochastic systems driven by Gaussian noise. Of particular importance are systems driven by fractional Brownian motion (fBm), and other long-memory and/or self-similar noise models. Classical probabilistic tools cannot be used to analyze fBm, because it fails to have the martingale and Markov property. In recent years, there have been major breakthroughs in integration theory for fBm, particularly in rough path, fractional calculus, and random dynamical systems. This special session will be devoted to have a discussion about these various techniques and to what extent they can be used jointly. Employing these theories to solve dependent-noise-driven SDEs and SPDEs will be the first main goal of this session, as well as the study of stability properties of the solutions by using the theory of random dynamical systems. The second goal will be to bring together the theoretical and applied community of researchers in order to bridge the gap between theory and applications. On the applied side, a particular attention will be devoted to porous media and data assimilation.
List of approved abstract