Department of Mathematics


  •  Shlomo Levental, MSU
  •  Poincare type inequalities via 1-dimensional Malliavin calculus
  •  03/21/2019
  •  3:00 PM - 3:50 PM
  •  C405 Wells Hall

We will review briefly 3 types of operators which are mapping spaces of real-valued functions which are defined on the real line equipped with standard normal probability measure. Those are the derivative, divergence and Ornstein-Uklenbeck operators. There are simple formulas that describe the relationships between those operators. Using those formulas the proofs of the following will be presented: 1. Poincare inequality : The variance of a function of N(0,1) is dominated by the second moment of its derivative. 2. An upper bound to the Wasserstein distance between the distribution of a function of N(0,1) (the function has mean 0 and standard deviation 1) and N(0,1) itself. This upper bound is (up to a constant) the multiplication of the L4 norm of the function derivative and the L4 norm of the function 2nd derivative. The material is based on Nourdin and Peccati book.



Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

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