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Six Lectures on Stochastic Variational Analysis

Special Events

Speaker: Roger Wets, UC Davis
Location: 2240 MSB
Start time: Thu, Feb 16 2012, 10:30AM

“Stochastic Variational Analysis” emerged in response to the need of solving, at least approximately, (generalized) equations systems, optimization and variational problems whose defining parameters are, at least in part, stochastic. Problems of this type arise in stochastic optimization, stochastic equilibrium problems, uncertainty quantification, statistical estimation problems that turn up in a broad variety of engineering, economics, finance, energy networks, signal processing, ecology and biological problems. These lectures will be introductory in nature. Because the solutions to such systems aren’t gen- erally unique, one can’t rely on classical probabilistic techniques to either describe their solutions or find (probabilistic) approximations that might, in turn, be based on standard laws of large numbers and associated asymptotic analysis. The foundations of the theory lies in an understanding of the geometry and the analytic (topolog- ical) properties of random sets, including a suitable translation to a functional setting, coupled with both appropriate laws of large numbers, i.e., what can be learned from large samples, and fundamental inequalities, i.e., what can be learned from small samples. This dual approach is fundamental to the potential applications of the theory in practical settings.

This will be a series of six lectures starting today and continuing weekly.