Shige Peng
Shandong University, China
Title: Why Gaussian distributions are widely applied under distribution uncertainties.
Why are Gaussian distributions actually widely used in our real world in which probability and statistic model uncertainties are clearly strong? In this talk we will present the author's result of a new central limit theorem: under the upper (or robust, sublinear) expectation over the uncertainty subset of probabilities, we still have the corresponding central limit theorem (CLM). This result tells us that in many important situations we can still use the classical Gaussian distribution to calculate E[u(X)]. But the choice of the variance sensitively depends on whether the above function u is convex or concave. If u is neither convex nor concave then the situation becomes more subtle and a new calculation method is introduced for this G-normal distribution. We also present the dynamic (thus infinite-dimensional) counterpart of the problem which gives us a new type of Brownian motion, called G-Brownian motion, and its corresponding Ito calculus.
©2008, Department of Mathematical Sciences
Last Modified: November 18, 2008