Math 191a
 
Stochastic Analysis
Fall 2012-13
 
TR 10:30 AM, 257 Sloan
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Instructor:  Tom Alberts, 258 Sloan, 626-395-4339.



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This course will describe the basic tools of stochastic analysis and their applications in probability, while at the same time discussing their analogues in quantum physics. With the proper background the probabilistic description of these tools is relatively transparent and simple. The main topics to be discussed include Gaussian Hilbert Spaces, Wiener chaos, Wick products, hypercontractivity, and Cameron-Martin shifts. The ultimate goal of the course is to gain a working understanding of the Malliavin calculus, which is usually described as the stochastic calculus of variations (i.e. variational formulas over functions in Wiener space). A strong background in analysis will be assumed. A good background in probability would be helpful but a working knowledge of multi-dimensional Gaussians will probably be sufficient.



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