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Jose H. Blanchet - Columbia University
Title: Strong Monte Carlo for Multidimensional SDEs via Rough Path Analysis.Abstract: Underlying there is a multidimensional SDE X(.) driven by Brownian motion. A strongly simulatable approximation to X(.) is a sequence of process {X_n(.)} which are piece-wise constant, with finitely many discountinuities for each n, and such that the uniform norm between X(.) and X_n(.) in the compact set [0,1] is less than 1/n with probability one. The probability one statement is crucial. Strong Monte Carlo approximations have been known basically for one dimensional diffusions and related processes. We provide the first strong simulatable approximations for multidimensional SDEs. The construction leverages off the theory of rough paths, and novel simulation techniques of times that look into the infinite future of a sequence of information often used to approximate SDEs.
When | 4:00 pm to 5:00 pm on Thursday, September 11, 2014 |
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Location | MCS 148 |