SEMINAR

Markov finite approximations of Markov operators: theory and estimates

Department of Mathematics
University of Southern Mississippi

ABSTRACT

A linear operator on an L^1-space is called a Markov operator if it maps density functions to density functions. Markov operators are widely used in every field of stochastic analysis, e.g., applied probability, ergodic theory, and random perturbations. So the mathematical analysis of numerical methods for approximating Markov operators is important in theory and applications.

Let P be a Markov operator on L^1(C), where C = [0,1]^N is the unit N-cube. Using a standard triangulation of C, I construct a piecewise linear Markov finite approximation scheme. I'll list various nice properties of this method, such as the consistency and stability in both the L^1-norm and the BV-norm. An explicit constant of the uniform boundedness for the variation of functions is also obtained.

Some historical developments along this direction will be described, starting with the famous Ulam's piecewise constant approximation scheme for approximating Frobenius-Perron operators for chaotic dynamical systems.

WHERE: TEC 340

WHEN(day): Friday, April 23rd, 1999

WHEN(time): 2:00

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