Friday, July 19, 2013

1307.4814 (Jeremy T. Clark et al.)

Limit theorems resulting in a family of symmetric, scale-invariant
diffusions with singular coefficients

Jeremy T. Clark, Jeffrey H. Schenker
We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients in dimension one. A corresponding family of generalized characteristic functions provides a potentially useful tool for proving limit theorems resulting in the laws of the scale-invariant diffusions in analogy with the standard Gaussian theory. We apply the generalized characteristic functions in combination with a martingale construction to prove two simple invariance principles starting from an inhomogeneous diffusion and a nearest-neighbor random walk, respectively.
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