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arXiv · 1307.4814

Spectral analysis of a family of symmetric, scale-invariant diffusions with singular coefficients and associated limit theorems

Jeremy T. Clark·Jeffrey H. Schenker
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Abstract

We discuss a family of time-reversible, scale-invariant diffusions with singular coefficients. In analogy with the standard Gaussian theory, a corresponding family of generalized characteristic functions provides a useful tool for proving limit theorems resulting in non-Gaussian, scale-invariant diffusions. We apply the generalized characteristic functions in combination with a martingale construction to prove a simple invariance principle starting from a spatially inhomogeneous nearest-neighbor random walk.

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Jeremy T. Clark, Jeffrey H. Schenker. 2013-07-18. Spectral analysis of a family of symmetric, scale-invariant diffusions with singular coefficients and associated limit theorems. https://arxiv.org/abs/1307.4814

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