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Time-Reversible Diffusions

John Kent
Advances in Applied Probability
Vol. 10, No. 4 (Dec., 1978), pp. 819-835
DOI: 10.2307/1426661
Stable URL: http://www.jstor.org/stable/1426661
Page Count: 17
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Time-Reversible Diffusions
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Abstract

Symmetric diffusions on manifolds with boundary are studied. Symmetric diffusions are nicer to work with than non-symmetric diffusions because (1) it is easier to tell if an equilibrium density exists, and (2) it is easier to find the equilibrium density when it does exist. If an equilibrium density exists, a symmetric diffusion is time reversible. On the line essentially all diffusions are symmetric. Using symmetric diffusions, it is shown that a large family of densities can be realized as equilibrium densities of time-reversible diffusions. Some examples are given.

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