Date:

Monday, April 15, 2002

Speaker:

Dr. Alexander Veretennikov

Affiliation:

Department of Mathematics
University of Kansas

Contact Information

veretennikov@math.ukans.edu

Title:

On Approximations of Heat Type Equations

Abstract:

Ergodic heat equations with a parameter are considered. The first approximation result establishes a smooth dependence of invariant measure or its integral functional on a parameter. This means that if one has an approximation with a simple formula for the invariant measure it is close to the original one along with several derivatives (the order depends on assumptions). The second approximation result states that the heat equation kernel, or fundamental solution, can be also approximated using Bernoulli trials or Markov chains on a lattice. There is also a version concerning approximations of exponentially decreasing solutions for the equation with a nonrandom potential."