Basic Estimates of Stability Rate for One-dimensional Diffusions

Details Basic Estimates of Stability Rate for One-dimensional Diffusions Basic Estimates of Stability Rate for One-dimensional Diffusions

2011-11-29

arxiv.org/abs/1111.6659v1

Chapter 6 in "Probability Approximations and Beyond'', Lecture Notes in Statistics 205, 2012

Mathematics

Probability

24 pages

Scientific paper

In the context of one-dimensional diffusions, we present basic estimates (having the same lower and upper bounds with a factor of 4 only) for four Poincar\'e-type (or Hardy-type) inequalities. The derivation of two estimates have been open problems for quite some time. The bounds provide exponentially ergodic or decay rates. We refine the bounds and illustrate them with typical examples.

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